%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU218+3 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:55:58 PM UTC 2026
% Result : Theorem 90.88s 18.68s
% Output : CNFRefutation 91.62s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f4,axiom,
! [X0] :
( ( function(X0)
& empty(X0)
& relation(X0) )
=> ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f7,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(f8,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(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f11,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f12,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f13,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f14,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_relat_1) ).
fof(f18,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f19,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f22,axiom,
! [X0] :
( ( one_to_one(X0)
& function(X0)
& relation(X0) )
=> ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
fof(f24,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f25,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f26,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f27,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f28,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f30,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f31,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f32,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f33,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f34,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f35,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f36,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f37,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f38,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f41,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f42,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f43,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f45,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f46,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) )
=> ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f47,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) )
=> ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f48,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f49,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f50,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f51,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f52,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
<~> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f53,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
<~> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f57,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f61,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f66,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,[],[f7]) ).
fof(f67,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,[],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f69,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f70,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_inverse(X0))
& relation(relation_inverse(X0)) ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| ( one_to_one(X0)
& function(X0)
& relation(X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f75,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f80,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f45]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0] :
( empty(X0)
| ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f85,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0] :
( ~ empty(X0)
| ( relation(relation_inverse(X0))
& empty(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f87,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(ennf_transformation,[],[f14]) ).
fof(f88,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f89,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f90,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f49]) ).
fof(f96,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( function_inverse(X0) != X1
| ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1) ) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f97,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( function_inverse(X0) != X1
| ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1) ) ) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( function_inverse(X0) != X1
| ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
( function(sK1)
& relation(sK1)
& one_to_one(sK1)
& function(sK2)
& relation(sK2)
& ( sK2 = function_inverse(sK1)
| ( ! [X4,X5] :
( sP0(sK1,X4,X5,sK2)
& ( apply(sK2,X4) != X5
| ~ in(X4,relation_rng(sK1))
| ( apply(sK1,X5) = X4
& in(X5,relation_dom(sK1)) ) ) )
& relation_rng(sK1) = relation_dom(sK2) ) )
& ( sK2 != function_inverse(sK1)
| ~ sP0(sK1,sK3,sK4,sK2)
| ( sK4 = apply(sK2,sK3)
& in(sK3,relation_rng(sK1))
& ( sK3 != apply(sK1,sK4)
| ~ in(sK4,relation_dom(sK1)) ) )
| relation_rng(sK1) != relation_dom(sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f98]) ).
fof(f100,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,[],[f64]) ).
fof(f101,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,[],[f100]) ).
fof(f102,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_dom(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(X5,sK7(X0,X5)),X0) )
& ( ! [X6] : ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK5(X0,X1),X1)
| in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0) )
& ( ~ in(sK5(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(sK5(X0,X1),X3),X0) ) )
| X1 = relation_dom(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X4,sK6(X0,X1)),skolemize(X7,sK7(X0,X5))],[f101]) ).
fof(f103,plain,
( function(sK8)
& empty(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f34]) ).
fof(f104,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f30]) ).
fof(f105,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,[],[f67]) ).
fof(f106,plain,
( relation(sK10)
& ~ empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f35]) ).
fof(f107,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f31]) ).
fof(f108,plain,
( one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f38]) ).
fof(f109,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] : in(ordered_pair(X3,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f110,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] : in(ordered_pair(X7,X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] : in(ordered_pair(X4,X2),X0) )
& ( ~ in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| in(ordered_pair(sK15(X0,X5),X5),X0) )
& ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ) ) )
& ( ( ( in(sK13(X0,X1),X1)
| in(ordered_pair(sK14(X0,X1),sK13(X0,X1)),X0) )
& ( ~ in(sK13(X0,X1),X1)
| ! [X3] : ~ in(ordered_pair(X3,sK13(X0,X1)),X0) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X2,sK13(X0,X1)),skolemize(X4,sK14(X0,X1)),skolemize(X7,sK15(X0,X5))],[f110]) ).
fof(f112,plain,
~ empty(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f37]) ).
fof(f113,plain,
empty(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f33]) ).
fof(f114,plain,
! [X0] :
( empty(sK18(X0))
& element(sK18(X0),powerset(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X1,sK18(X0))],[f36]) ).
fof(f115,plain,
! [X0] :
( empty(X0)
| ( ~ empty(sK19(X0))
& element(sK19(X0),powerset(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X1,sK19(X0))],[f84]) ).
fof(f116,plain,
! [X0] : element(sK20(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f15]) ).
fof(f117,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f118,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X3,X2),X0) )
& ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( relation_inverse(X0) != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) )
& ( ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ) ) )
& ( ( ( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0) )
& ( ~ in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ~ in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0) ) )
| X1 = relation_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X2,sK21(X0,X1)),skolemize(X3,sK22(X0,X1))],[f118]) ).
fof(f120,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f121,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ? [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X2,X3),X1) )
& ( ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| X0 = X1 ) ) ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ( ( X0 != X1
| ! [X4,X5] :
( ( ~ in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X4,X5),X1) )
& ( ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X4,X5),X0) ) ) )
& ( ( ( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1) )
& ( ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1) ) )
| X0 = X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X2,sK23(X0,X1)),skolemize(X3,sK24(X0,X1))],[f121]) ).
fof(f128,plain,
function(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f129,plain,
relation(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f130,plain,
one_to_one(sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f131,plain,
function(sK2),
inference(cnf_transformation,[],[f99]) ).
fof(f132,plain,
relation(sK2),
inference(cnf_transformation,[],[f99]) ).
fof(f133,plain,
! [X4,X5] :
( sK2 = function_inverse(sK1)
| sP0(sK1,X4,X5,sK2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f134,plain,
! [X4,X5] :
( sK2 = function_inverse(sK1)
| apply(sK2,X4) != X5
| ~ in(X4,relation_rng(sK1))
| apply(sK1,X5) = X4 ),
inference(cnf_transformation,[],[f99]) ).
fof(f135,plain,
! [X4,X5] :
( sK2 = function_inverse(sK1)
| apply(sK2,X4) != X5
| ~ in(X4,relation_rng(sK1))
| in(X5,relation_dom(sK1)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f136,plain,
( sK2 = function_inverse(sK1)
| relation_rng(sK1) = relation_dom(sK2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f137,plain,
( sK2 != function_inverse(sK1)
| ~ sP0(sK1,sK3,sK4,sK2)
| sK4 = apply(sK2,sK3)
| relation_rng(sK1) != relation_dom(sK2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f138,plain,
( sK2 != function_inverse(sK1)
| ~ sP0(sK1,sK3,sK4,sK2)
| in(sK3,relation_rng(sK1))
| relation_rng(sK1) != relation_dom(sK2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f139,plain,
( sK2 != function_inverse(sK1)
| ~ sP0(sK1,sK3,sK4,sK2)
| sK3 != apply(sK1,sK4)
| ~ in(sK4,relation_dom(sK1))
| relation_rng(sK1) != relation_dom(sK2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f140,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f141,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f142,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f144,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f145,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f146,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f147,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f148,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f149,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f150,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(X5,sK7(X0,X5)),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f151,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_dom(X0) != X1
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f152,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK5(X0,X1),X1)
| in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f153,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(ordered_pair(sK5(X0,X1),X3),X0)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[],[f102]) ).
fof(f154,plain,
function(sK8),
inference(cnf_transformation,[],[f103]) ).
fof(f155,plain,
empty(sK8),
inference(cnf_transformation,[],[f103]) ).
fof(f156,plain,
relation(sK8),
inference(cnf_transformation,[],[f103]) ).
fof(f157,plain,
function(sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f158,plain,
relation(sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f159,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) != X2
| empty_set = X2 ),
inference(cnf_transformation,[],[f105]) ).
fof(f162,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,[],[f105]) ).
fof(f163,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,[],[f105]) ).
fof(f164,plain,
relation(sK10),
inference(cnf_transformation,[],[f106]) ).
fof(f165,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f106]) ).
fof(f166,plain,
relation(sK11),
inference(cnf_transformation,[],[f107]) ).
fof(f167,plain,
empty(sK11),
inference(cnf_transformation,[],[f107]) ).
fof(f168,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f169,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
function(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
relation(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f172,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f173,plain,
! [X0] :
( ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f174,plain,
! [X0] :
( ~ function(X0)
| ~ empty(X0)
| ~ relation(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f177,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_rng(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f178,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f179,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f180,plain,
! [X0,X1,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(ordered_pair(sK15(X0,X5),X5),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f181,plain,
! [X0,X1,X6,X5] :
( ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f182,plain,
! [X0,X1] :
( ~ relation(X0)
| in(sK13(X0,X1),X1)
| in(ordered_pair(sK14(X0,X1),sK13(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f183,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| ~ in(sK13(X0,X1),X1)
| ~ in(ordered_pair(X3,sK13(X0,X1)),X0)
| relation_rng(X0) = X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f184,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f185,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f186,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f187,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f112]) ).
fof(f188,plain,
empty(sK17),
inference(cnf_transformation,[],[f113]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f191,plain,
! [X0] : empty(sK18(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f192,plain,
! [X0] : element(sK18(X0),powerset(X0)),
inference(cnf_transformation,[],[f114]) ).
fof(f193,plain,
! [X0] :
( empty(X0)
| ~ empty(sK19(X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f194,plain,
! [X0] :
( empty(X0)
| element(sK19(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f195,plain,
! [X0] : element(sK20(X0),X0),
inference(cnf_transformation,[],[f116]) ).
fof(f196,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f198,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f86]) ).
fof(f199,plain,
! [X0] :
( ~ relation(X0)
| relation(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f87]) ).
fof(f200,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X4,X5),X1)
| in(ordered_pair(X5,X4),X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f201,plain,
! [X0,X1,X4,X5] :
( ~ relation(X0)
| ~ relation(X1)
| relation_inverse(X0) != X1
| ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f202,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f203,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ~ in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f119]) ).
fof(f204,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f207,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f208,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f209,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f210,plain,
relation(empty_set),
inference(cnf_transformation,[],[f24]) ).
fof(f212,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f213,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f217,plain,
! [X4] :
( sK2 = function_inverse(sK1)
| ~ in(X4,relation_rng(sK1))
| in(apply(sK2,X4),relation_dom(sK1)) ),
inference(equality_resolution,[],[f135]) ).
fof(f218,plain,
! [X4] :
( sK2 = function_inverse(sK1)
| ~ in(X4,relation_rng(sK1))
| apply(sK1,apply(sK2,X4)) = X4 ),
inference(equality_resolution,[],[f134]) ).
fof(f219,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f151]) ).
fof(f220,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_dom(X0))
| in(ordered_pair(X5,sK7(X0,X5)),X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f221,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f162]) ).
fof(f223,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(equality_resolution,[],[f160]) ).
fof(f224,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f181]) ).
fof(f225,plain,
! [X0,X5] :
( ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(ordered_pair(sK15(X0,X5),X5),X0) ),
inference(equality_resolution,[],[f180]) ).
fof(f226,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(ordered_pair(X5,X4),X0)
| in(ordered_pair(X4,X5),relation_inverse(X0)) ),
inference(equality_resolution,[],[f201]) ).
fof(f227,plain,
! [X0,X4,X5] :
( ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(ordered_pair(X4,X5),relation_inverse(X0))
| in(ordered_pair(X5,X4),X0) ),
inference(equality_resolution,[],[f200]) ).
tcf(c_54,negated_conjecture,
( ~ in(sK4,relation_dom(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( function_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) )
| ( apply(sK1,sK4) != sK3 ) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_55,negated_conjecture,
( in(sK3,relation_rng(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( function_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_56,negated_conjecture,
( ( apply(sK2,sK3) = sK4 )
| ~ sP0(sK1,sK3,sK4,sK2)
| ( function_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_57,negated_conjecture,
( ( function_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = relation_dom(sK2) ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( in(apply(sK2,X0),relation_dom(sK1))
| ( function_inverse(sK1) = sK2 )
| ~ in(X0,relation_rng(sK1)) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( ( function_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,X0)) = X0 )
| ~ in(X0,relation_rng(sK1)) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_60,negated_conjecture,
! [X0: $i,X1: $i] :
( sP0(sK1,X0,X1,sK2)
| ( function_inverse(sK1) = sK2 ) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_61,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f132]) ).
tcf(c_62,negated_conjecture,
function(sK2),
inference(cnf_transformation,[],[f131]) ).
tcf(c_63,negated_conjecture,
one_to_one(sK1),
inference(cnf_transformation,[],[f130]) ).
tcf(c_64,negated_conjecture,
relation(sK1),
inference(cnf_transformation,[],[f129]) ).
tcf(c_65,negated_conjecture,
function(sK1),
inference(cnf_transformation,[],[f128]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_71,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_72,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = relation_dom(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_73,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_74,plain,
! [X0: $i] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_75,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(ordered_pair(sK5(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK7(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_80,plain,
relation(sK8),
inference(cnf_transformation,[],[f156]) ).
tcf(c_81,plain,
empty(sK8),
inference(cnf_transformation,[],[f155]) ).
tcf(c_82,plain,
function(sK8),
inference(cnf_transformation,[],[f154]) ).
tcf(c_83,plain,
relation(sK9),
inference(cnf_transformation,[],[f158]) ).
tcf(c_84,plain,
function(sK9),
inference(cnf_transformation,[],[f157]) ).
tcf(c_85,plain,
! [X0: $i] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_86,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,[],[f163]) ).
tcf(c_87,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,[],[f221]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_90,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f165]) ).
tcf(c_91,plain,
relation(sK10),
inference(cnf_transformation,[],[f164]) ).
tcf(c_92,plain,
empty(sK11),
inference(cnf_transformation,[],[f167]) ).
tcf(c_93,plain,
relation(sK11),
inference(cnf_transformation,[],[f166]) ).
tcf(c_94,plain,
! [X0: $i] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_95,plain,
relation(sK12),
inference(cnf_transformation,[],[f171]) ).
tcf(c_96,plain,
function(sK12),
inference(cnf_transformation,[],[f170]) ).
tcf(c_97,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f169]) ).
tcf(c_98,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_99,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_100,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_101,plain,
! [X0: $i] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_102,plain,
! [X0: $i] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_103,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(X1) = X2 )
| ~ relation(X1)
| ~ in(sK13(X1,X2),X2)
| ~ in(ordered_pair(X0,sK13(X1,X2)),X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| in(ordered_pair(sK14(X0,X1),sK13(X0,X1)),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK15(X1,X0),X0),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_108,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_109,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_110,plain,
! [X0: $i] :
( ( function_inverse(X0) = relation_inverse(X0) )
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_111,plain,
~ empty(sK16),
inference(cnf_transformation,[],[f187]) ).
tcf(c_112,plain,
empty(sK17),
inference(cnf_transformation,[],[f188]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_115,plain,
! [X0: $i] : element(sK18(X0),powerset(X0)),
inference(cnf_transformation,[],[f192]) ).
tcf(c_116,plain,
! [X0: $i] : empty(sK18(X0)),
inference(cnf_transformation,[],[f191]) ).
tcf(c_117,plain,
! [X0: $i] :
( empty(X0)
| element(sK19(X0),powerset(X0)) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_118,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(sK19(X0)) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_119,plain,
! [X0: $i] : element(sK20(X0),X0),
inference(cnf_transformation,[],[f195]) ).
tcf(c_120,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_121,plain,
! [X0: $i] :
( empty(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_122,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_123,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ~ in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X0),relation_inverse(X2))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X0),X2)
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),relation_inverse(X2)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f204]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ~ in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_133,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_135,plain,
relation(empty_set),
inference(cnf_transformation,[],[f210]) ).
tcf(c_136,plain,
empty(empty_set),
inference(cnf_transformation,[],[f212]) ).
tcf(c_137,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f213]) ).
tcf(c_145,plain,
( empty(relation_inverse(sK1))
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_148,plain,
( empty(relation_rng(sK1))
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_160,plain,
( empty(sK1)
| ~ relation(sK1)
| ~ empty(relation_dom(sK1)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_168,plain,
( function(relation_inverse(sK1))
| ~ one_to_one(sK1)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_173,plain,
( ( function_inverse(sK1) = relation_inverse(sK1) )
| ~ one_to_one(sK1)
| ~ function(sK1)
| ~ relation(sK1) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_193,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_100,c_94,c_85,c_100]) ).
tcf(c_195,plain,
! [X0: $i] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_123]) ).
tcf(c_197,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_86,c_78,c_86]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X0),relation_inverse(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_126,c_195]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(ordered_pair(X1,X0),X2)
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),relation_inverse(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_127,c_195]) ).
tcf(c_954,plain,
! [X0: $i,X1: $i] :
( ( function_inverse(X1) = relation_inverse(X1) )
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_110]) ).
tcf(c_955,plain,
! [X0: $i] :
( ( function_inverse(X0) = relation_inverse(X0) )
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_954]) ).
tcf(c_957,plain,
! [X0: $i] :
( ( function_inverse(X0) = relation_inverse(X0) )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_955,c_94,c_85,c_110,c_193]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i] :
( function(relation_inverse(X1))
| ~ empty(X0)
| ~ function(X1)
| ~ relation(X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_193,c_99]) ).
tcf(c_967,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(unflattening,[status(thm)],[c_966]) ).
tcf(c_969,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_967,c_94,c_85,c_967]) ).
tcf(c_978,plain,
! [X0: $i] :
( ( function_inverse(X0) = relation_inverse(X0) )
| ~ function(X0)
| ~ relation(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_110]) ).
tcf(c_979,plain,
( ( function_inverse(sK1) = relation_inverse(sK1) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(unflattening,[status(thm)],[c_978]) ).
tcf(c_980,plain,
function_inverse(sK1) = relation_inverse(sK1),
inference(global_subsumption_just,[status(thm)],[c_979,c_65,c_64,c_63,c_173]) ).
tcf(c_985,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_99]) ).
tcf(c_986,plain,
( function(relation_inverse(sK1))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(unflattening,[status(thm)],[c_985]) ).
tcf(c_987,plain,
function(relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_986,c_65,c_64,c_63,c_168]) ).
tcf(c_992,plain,
! [X0: $i] :
( ( function_inverse(X0) = relation_inverse(X0) )
| ~ function(X0)
| ~ relation(X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_110]) ).
tcf(c_993,plain,
( ( function_inverse(sK12) = relation_inverse(sK12) )
| ~ function(sK12)
| ~ relation(sK12) ),
inference(unflattening,[status(thm)],[c_992]) ).
tcf(c_994,plain,
function_inverse(sK12) = relation_inverse(sK12),
inference(global_subsumption_just,[status(thm)],[c_993,c_96,c_95,c_993]) ).
tcf(c_999,plain,
! [X0: $i] :
( function(relation_inverse(X0))
| ~ function(X0)
| ~ relation(X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_97,c_99]) ).
tcf(c_1000,plain,
( function(relation_inverse(sK12))
| ~ function(sK12)
| ~ relation(sK12) ),
inference(unflattening,[status(thm)],[c_999]) ).
tcf(c_1001,plain,
function(relation_inverse(sK12)),
inference(global_subsumption_just,[status(thm)],[c_1000,c_96,c_95,c_1000]) ).
tcf(c_1706,plain,
! [X0: $i,X1: $i] :
( sP0(sK1,X0,X1,sK2)
| ( relation_inverse(sK1) = sK2 ) ),
inference(light_normalisation,[status(thm)],[c_60,c_980]) ).
tcf(c_1713,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = relation_dom(sK2) ) ),
inference(light_normalisation,[status(thm)],[c_57,c_980]) ).
tcf(c_1784,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_rng(sK1)) ),
inference(light_normalisation,[status(thm)],[c_58,c_980]) ).
tcf(c_1810,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,X0)) = X0 )
| ~ in(X0,relation_rng(sK1)) ),
inference(light_normalisation,[status(thm)],[c_59,c_980]) ).
tcf(c_1864,plain,
( in(sK3,relation_rng(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(light_normalisation,[status(thm)],[c_55,c_980]) ).
tcf(c_1877,plain,
( ( apply(sK2,sK3) = sK4 )
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(light_normalisation,[status(thm)],[c_56,c_980]) ).
tcf(c_1930,plain,
( ~ in(sK4,relation_dom(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) )
| ( apply(sK1,sK4) != sK3 ) ),
inference(light_normalisation,[status(thm)],[c_54,c_980]) ).
tcf(c_2161,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| ~ empty(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3169,plain,
function(sK11),
inference(superposition,[status(thm)],[c_92,c_85]) ).
tcf(c_3170,plain,
function(sK17),
inference(superposition,[status(thm)],[c_112,c_85]) ).
tcf(c_3171,plain,
! [X0: $i] : function(sK18(X0)),
inference(superposition,[status(thm)],[c_116,c_85]) ).
tcf(c_3172,plain,
function(empty_set),
inference(superposition,[status(thm)],[c_136,c_85]) ).
tcf(c_3180,plain,
relation(sK17),
inference(superposition,[status(thm)],[c_112,c_94]) ).
tcf(c_3181,plain,
! [X0: $i] : relation(sK18(X0)),
inference(superposition,[status(thm)],[c_116,c_94]) ).
tcf(c_3190,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK2)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ relation(sK1)
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_1713,c_296]) ).
tcf(c_3191,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_inverse(X2),X1) = X0 )
| ~ relation(X2)
| ~ function(relation_inverse(X2))
| ~ relation(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_197]) ).
tcf(c_3192,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK2)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3190,c_64]) ).
tcf(c_3208,plain,
! [X0: $i] :
( function(relation_dom(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_85]) ).
tcf(c_3221,plain,
! [X0: $i] :
( function(relation_rng(X0))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_85]) ).
tcf(c_3237,plain,
( empty(sK2)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_1713,c_121]) ).
tcf(c_3282,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_1784,c_67]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X2)
| ~ empty(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_67]) ).
tcf(c_3299,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK1)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ relation(sK1)
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_1713,c_297]) ).
tcf(c_3300,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK1)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3299,c_64]) ).
tcf(c_3309,plain,
! [X0: $i] :
( element(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_1784,c_69]) ).
tcf(c_3310,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(ordered_pair(X1,X0),relation_inverse(X2))
| ~ relation(X2)
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_69]) ).
tcf(c_3327,plain,
! [X0: $i] :
( ( relation_dom(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_133]) ).
tcf(c_3328,plain,
sK8 = empty_set,
inference(superposition,[status(thm)],[c_81,c_133]) ).
tcf(c_3329,plain,
empty_set = sK11,
inference(superposition,[status(thm)],[c_92,c_133]) ).
tcf(c_3330,plain,
! [X0: $i] :
( ( relation_rng(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_133]) ).
tcf(c_3331,plain,
empty_set = sK17,
inference(superposition,[status(thm)],[c_112,c_133]) ).
tcf(c_3332,plain,
! [X0: $i] : sK18(X0) = empty_set,
inference(superposition,[status(thm)],[c_116,c_133]) ).
tcf(c_3333,plain,
! [X0: $i] :
( ( relation_inverse(X0) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_133]) ).
tcf(c_3350,plain,
! [X0: $i] : element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[c_115,c_3332]) ).
tcf(c_3363,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_rng(sK1))
| ~ in(relation_dom(sK1),apply(sK2,X0)) ),
inference(superposition,[status(thm)],[c_1784,c_70]) ).
tcf(c_3364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(relation_inverse(X0),ordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_296,c_70]) ).
tcf(c_3401,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3327]) ).
tcf(c_3402,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3327]) ).
tcf(c_3403,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3327]) ).
tcf(c_3404,plain,
relation_dom(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3327]) ).
tcf(c_3421,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3330]) ).
tcf(c_3422,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3330]) ).
tcf(c_3423,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3330]) ).
tcf(c_3424,plain,
relation_rng(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3330]) ).
tcf(c_3447,plain,
! [X0: $i] :
( empty(X0)
| empty(powerset(X0))
| in(sK19(X0),powerset(X0)) ),
inference(superposition,[status(thm)],[c_117,c_68]) ).
tcf(c_3448,plain,
! [X0: $i] :
( empty(X0)
| in(sK20(X0),X0) ),
inference(superposition,[status(thm)],[c_119,c_68]) ).
tcf(c_3450,plain,
! [X0: $i] :
( empty(powerset(X0))
| in(empty_set,powerset(X0)) ),
inference(superposition,[status(thm)],[c_3350,c_68]) ).
tcf(c_3453,plain,
! [X0: $i] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_3450,c_137]) ).
tcf(c_3454,plain,
! [X0: $i] :
( empty(X0)
| in(sK19(X0),powerset(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3447,c_137]) ).
tcf(c_3476,plain,
! [X0: $i] : ~ in(powerset(X0),empty_set),
inference(superposition,[status(thm)],[c_3453,c_70]) ).
tcf(c_3484,plain,
( empty(relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3448,c_3282]) ).
tcf(c_3485,plain,
( empty(relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3448,c_1810]) ).
tcf(c_3486,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK20(X0)) ),
inference(superposition,[status(thm)],[c_3448,c_70]) ).
tcf(c_3502,plain,
! [X0: $i] :
( empty(X0)
| ~ in(powerset(X0),sK19(X0)) ),
inference(superposition,[status(thm)],[c_3454,c_70]) ).
tcf(c_3514,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_rng(sK1)) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3485,c_3330]) ).
tcf(c_3515,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_rng(sK1)) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3485,c_3327]) ).
tcf(c_3516,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3485,c_133]) ).
tcf(c_3517,plain,
( relation(relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3485,c_94]) ).
tcf(c_3518,plain,
( function(relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3485,c_85]) ).
tcf(c_3519,plain,
( empty(sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_3485,c_103]) ).
tcf(c_3526,plain,
( empty(sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3519,c_64]) ).
tcf(c_3546,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3526,c_3327]) ).
tcf(c_3547,plain,
( ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3526,c_133]) ).
tcf(c_3569,plain,
( empty(relation_rng(sK1))
| ~ empty(relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_3484,c_64,c_148,c_160]) ).
tcf(c_3575,plain,
( empty(relation_rng(sK1))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_73,c_3569]) ).
tcf(c_3608,plain,
( relation(relation_inverse(sK1))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_980,c_108]) ).
tcf(c_3609,plain,
( relation(relation_inverse(sK12))
| ~ function(sK12)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_994,c_108]) ).
tcf(c_3610,plain,
relation(relation_inverse(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_3609,c_96,c_95]) ).
tcf(c_3611,plain,
relation(relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_3608,c_65,c_64]) ).
tcf(c_3624,plain,
relation_inverse(relation_inverse(sK2)) = sK2,
inference(superposition,[status(thm)],[c_61,c_120]) ).
tcf(c_3625,plain,
relation_inverse(relation_inverse(sK1)) = sK1,
inference(superposition,[status(thm)],[c_64,c_120]) ).
tcf(c_3626,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(X0))) = relation_dom(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_120]) ).
tcf(c_3627,plain,
relation_inverse(relation_inverse(sK9)) = sK9,
inference(superposition,[status(thm)],[c_83,c_120]) ).
tcf(c_3628,plain,
relation_inverse(relation_inverse(sK10)) = sK10,
inference(superposition,[status(thm)],[c_91,c_120]) ).
tcf(c_3629,plain,
relation_inverse(relation_inverse(sK12)) = sK12,
inference(superposition,[status(thm)],[c_95,c_120]) ).
tcf(c_3630,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_120]) ).
tcf(c_3631,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_120]) ).
tcf(c_3632,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(X0))) = relation_rng(X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_120]) ).
tcf(c_3633,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(function_inverse(X0))) = function_inverse(X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_120]) ).
tcf(c_3634,plain,
relation_inverse(relation_inverse(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_135,c_120]) ).
tcf(c_3635,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_rng(sK1))) = relation_rng(sK1) )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3517,c_120]) ).
tcf(c_3661,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_66]) ).
tcf(c_3662,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_66]) ).
tcf(c_3663,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X0) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_66]) ).
tcf(c_3665,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3526,c_66]) ).
tcf(c_3666,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3485,c_66]) ).
tcf(c_3684,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_3663]) ).
tcf(c_3687,plain,
relation_inverse(relation_inverse(relation_inverse(sK12))) = relation_inverse(sK12),
inference(superposition,[status(thm)],[c_3610,c_120]) ).
tcf(c_3690,plain,
relation_inverse(relation_inverse(relation_inverse(sK1))) = relation_inverse(sK1),
inference(superposition,[status(thm)],[c_3611,c_120]) ).
tcf(c_3695,plain,
( empty(sK2)
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3624,c_121]) ).
tcf(c_3696,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3624,c_297]) ).
tcf(c_3697,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3624,c_296]) ).
tcf(c_3708,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_rng(sK1) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_1713,c_3625]) ).
tcf(c_3712,plain,
( empty(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3625,c_121]) ).
tcf(c_3713,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3625,c_297]) ).
tcf(c_3714,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK1)
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3625,c_296]) ).
tcf(c_3719,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK1)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3714,c_3611]) ).
tcf(c_3722,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3713,c_3611]) ).
tcf(c_3737,plain,
( empty(sK1)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_1713,c_3712]) ).
tcf(c_3749,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK2)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ relation(sK2)
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3708,c_297]) ).
tcf(c_3750,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK1)
| ( relation_rng(sK1) = relation_dom(sK2) )
| ~ relation(sK2)
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3708,c_296]) ).
tcf(c_3772,plain,
! [X0: $i,X1: $i] :
( ~ in(ordered_pair(X1,X0),sK1)
| ~ in(relation_inverse(sK1),ordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_3722,c_70]) ).
tcf(c_3773,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X1,X0),relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_69]) ).
tcf(c_3774,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_67]) ).
tcf(c_3775,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X1) = X0 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_197]) ).
tcf(c_3784,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X1) = X0 )
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3775,c_987,c_3611]) ).
tcf(c_3805,plain,
relation_dom(relation_inverse(sK2)) = relation_rng(sK2),
inference(superposition,[status(thm)],[c_61,c_71]) ).
tcf(c_3806,plain,
relation_dom(relation_inverse(sK1)) = relation_rng(sK1),
inference(superposition,[status(thm)],[c_64,c_71]) ).
tcf(c_3807,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(X0))) = relation_rng(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_71]) ).
tcf(c_3808,plain,
relation_dom(relation_inverse(sK9)) = relation_rng(sK9),
inference(superposition,[status(thm)],[c_83,c_71]) ).
tcf(c_3809,plain,
relation_dom(relation_inverse(sK10)) = relation_rng(sK10),
inference(superposition,[status(thm)],[c_91,c_71]) ).
tcf(c_3810,plain,
relation_dom(relation_inverse(sK12)) = relation_rng(sK12),
inference(superposition,[status(thm)],[c_95,c_71]) ).
tcf(c_3811,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_71]) ).
tcf(c_3812,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = relation_rng(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_71]) ).
tcf(c_3813,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(X0))) = relation_rng(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_71]) ).
tcf(c_3814,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(function_inverse(X0))) = relation_rng(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_71]) ).
tcf(c_3815,plain,
relation_dom(relation_inverse(empty_set)) = relation_rng(empty_set),
inference(superposition,[status(thm)],[c_135,c_71]) ).
tcf(c_3816,plain,
relation_dom(relation_inverse(relation_inverse(sK1))) = relation_rng(relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_3611,c_71]) ).
tcf(c_3817,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_rng(sK1))) = relation_rng(relation_rng(sK1)) )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3517,c_71]) ).
tcf(c_3818,plain,
relation_dom(relation_inverse(relation_inverse(sK12))) = relation_rng(relation_inverse(sK12)),
inference(superposition,[status(thm)],[c_3610,c_71]) ).
tcf(c_3819,plain,
relation_dom(relation_inverse(empty_set)) = empty_set,
inference(light_normalisation,[status(thm)],[c_3815,c_3424]) ).
tcf(c_3820,plain,
relation_rng(relation_inverse(sK12)) = relation_dom(sK12),
inference(light_normalisation,[status(thm)],[c_3818,c_3629]) ).
tcf(c_3821,plain,
relation_rng(relation_inverse(sK1)) = relation_dom(sK1),
inference(light_normalisation,[status(thm)],[c_3816,c_3625]) ).
tcf(c_3845,plain,
relation_rng(relation_inverse(sK2)) = relation_dom(sK2),
inference(superposition,[status(thm)],[c_61,c_72]) ).
tcf(c_3847,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(X0))) = relation_dom(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_72]) ).
tcf(c_3848,plain,
relation_rng(relation_inverse(sK9)) = relation_dom(sK9),
inference(superposition,[status(thm)],[c_83,c_72]) ).
tcf(c_3849,plain,
relation_rng(relation_inverse(sK10)) = relation_dom(sK10),
inference(superposition,[status(thm)],[c_91,c_72]) ).
tcf(c_3851,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_72]) ).
tcf(c_3852,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = relation_dom(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_72]) ).
tcf(c_3853,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(X0))) = relation_dom(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_72]) ).
tcf(c_3854,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(function_inverse(X0))) = relation_dom(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_72]) ).
tcf(c_3855,plain,
relation_rng(relation_inverse(empty_set)) = relation_dom(empty_set),
inference(superposition,[status(thm)],[c_135,c_72]) ).
tcf(c_3856,plain,
relation_rng(relation_inverse(relation_inverse(sK1))) = relation_dom(relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_3611,c_72]) ).
tcf(c_3857,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_rng(sK1))) = relation_dom(relation_rng(sK1)) )
| ( apply(sK1,apply(sK2,sK20(relation_rng(sK1)))) = sK20(relation_rng(sK1)) ) ),
inference(superposition,[status(thm)],[c_3517,c_72]) ).
tcf(c_3858,plain,
relation_rng(relation_inverse(relation_inverse(sK12))) = relation_dom(relation_inverse(sK12)),
inference(superposition,[status(thm)],[c_3610,c_72]) ).
tcf(c_3859,plain,
relation_rng(relation_inverse(empty_set)) = empty_set,
inference(light_normalisation,[status(thm)],[c_3855,c_3404]) ).
tcf(c_3936,plain,
( empty(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3627,c_121]) ).
tcf(c_3937,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK9))
| ~ relation(relation_inverse(sK9))
| ~ in(ordered_pair(X0,X1),sK9) ),
inference(superposition,[status(thm)],[c_3627,c_297]) ).
tcf(c_3938,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK9)
| ~ relation(relation_inverse(sK9))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3627,c_296]) ).
tcf(c_3952,plain,
( empty(sK10)
| ~ empty(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3628,c_121]) ).
tcf(c_3953,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK10))
| ~ relation(relation_inverse(sK10))
| ~ in(ordered_pair(X0,X1),sK10) ),
inference(superposition,[status(thm)],[c_3628,c_297]) ).
tcf(c_3954,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK10)
| ~ relation(relation_inverse(sK10))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3628,c_296]) ).
tcf(c_3955,plain,
~ empty(relation_inverse(sK10)),
inference(forward_subsumption_resolution,[status(thm)],[c_3952,c_90]) ).
tcf(c_3966,plain,
! [X0: $i] :
( ~ empty(empty_set)
| ~ in(X0,empty_set) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_3972,plain,
( empty(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3629,c_121]) ).
tcf(c_3973,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3629,c_297]) ).
tcf(c_3974,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK12)
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3629,c_296]) ).
tcf(c_3977,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),sK12)
| ~ in(ordered_pair(X0,X1),relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3974,c_3610]) ).
tcf(c_3980,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3973,c_3610]) ).
tcf(c_3991,plain,
! [X0: $i] :
( empty(X0)
| ~ empty(empty_set)
| ( X0 != empty_set ) ),
inference(instantiation,[status(thm)],[c_2161]) ).
tcf(c_3992,plain,
( empty(sK1)
| ~ empty(empty_set)
| ( sK1 != empty_set ) ),
inference(instantiation,[status(thm)],[c_3991]) ).
tcf(c_3993,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( relation_rng(sK1) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_3708,c_3805]) ).
tcf(c_3994,plain,
( empty(relation_inverse(sK2))
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_75]) ).
tcf(c_3995,plain,
( function(relation_rng(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_3208]) ).
tcf(c_3996,plain,
( relation(relation_rng(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_74]) ).
tcf(c_3997,plain,
( empty(relation_rng(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_73]) ).
tcf(c_4013,plain,
relation_rng(sK1) = relation_dom(sK2),
inference(superposition,[status(thm)],[c_1713,c_3806]) ).
tcf(c_4014,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_rng(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3806,c_75]) ).
tcf(c_4015,plain,
( function(relation_rng(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3806,c_3208]) ).
tcf(c_4016,plain,
( relation(relation_rng(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3806,c_74]) ).
tcf(c_4017,plain,
( empty(relation_rng(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3806,c_73]) ).
tcf(c_4024,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_rng(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4014,c_3611]) ).
tcf(c_4027,plain,
( ~ in(sK4,relation_dom(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 )
| ( apply(sK1,sK4) != sK3 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1930,c_4013]) ).
tcf(c_4028,plain,
( ( apply(sK2,sK3) = sK4 )
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1877,c_4013]) ).
tcf(c_4029,plain,
( in(sK3,relation_rng(sK1))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1864,c_4013]) ).
tcf(c_4030,plain,
relation_dom(relation_inverse(sK1)) = relation_dom(sK2),
inference(demodulation,[status(thm)],[c_3806,c_4013]) ).
tcf(c_4031,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3515,c_4013]) ).
tcf(c_4032,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3514,c_4013]) ).
tcf(c_4033,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3516,c_4013]) ).
tcf(c_4034,plain,
( function(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3518,c_4013]) ).
tcf(c_4035,plain,
( relation(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3517,c_4013]) ).
tcf(c_4036,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_dom(sK1)) ),
inference(demodulation,[status(thm)],[c_3569,c_4013]) ).
tcf(c_4037,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3546,c_4013]) ).
tcf(c_4038,plain,
( ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3547,c_4013]) ).
tcf(c_4039,plain,
( empty(sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3526,c_4013]) ).
tcf(c_4040,plain,
( empty(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(demodulation,[status(thm)],[c_3485,c_4013]) ).
tcf(c_4041,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK1),apply(sK2,X0)) ),
inference(demodulation,[status(thm)],[c_3363,c_4013]) ).
tcf(c_4042,plain,
! [X0: $i] :
( element(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK2)) ),
inference(demodulation,[status(thm)],[c_3309,c_4013]) ).
tcf(c_4043,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(demodulation,[status(thm)],[c_3282,c_4013]) ).
tcf(c_4044,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,X0)) = X0 )
| ~ in(X0,relation_dom(sK2)) ),
inference(demodulation,[status(thm)],[c_1810,c_4013]) ).
tcf(c_4045,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK2)) ),
inference(demodulation,[status(thm)],[c_1784,c_4013]) ).
tcf(c_4105,plain,
( empty(relation_inverse(sK2))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_103]) ).
tcf(c_4106,plain,
( function(relation_dom(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_3221]) ).
tcf(c_4107,plain,
( relation(relation_dom(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_102]) ).
tcf(c_4108,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_101]) ).
tcf(c_4118,plain,
( empty(sK1)
| ~ relation(sK1)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4013,c_103]) ).
tcf(c_4119,plain,
( function(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4013,c_3221]) ).
tcf(c_4120,plain,
( relation(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4013,c_102]) ).
tcf(c_4121,plain,
( empty(relation_dom(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4013,c_101]) ).
tcf(c_4128,plain,
( empty(sK1)
| ~ empty(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4118,c_64]) ).
tcf(c_4135,plain,
( empty(sK1)
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_73,c_4128]) ).
tcf(c_4144,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_103]) ).
tcf(c_4145,plain,
( function(relation_dom(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_3221]) ).
tcf(c_4146,plain,
( relation(relation_dom(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_102]) ).
tcf(c_4147,plain,
( empty(relation_dom(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_101]) ).
tcf(c_4154,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4144,c_3611]) ).
tcf(c_4166,plain,
( function(relation_rng(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_121,c_3995]) ).
tcf(c_4169,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(light_normalisation,[status(thm)],[c_3635,c_4013]) ).
tcf(c_4201,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK20(powerset(X1))) ),
inference(superposition,[status(thm)],[c_119,c_113]) ).
tcf(c_4202,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3350,c_113]) ).
tcf(c_4215,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,sK19(X1)) ),
inference(superposition,[status(thm)],[c_117,c_114]) ).
tcf(c_4216,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK20(powerset(X1))) ),
inference(superposition,[status(thm)],[c_119,c_114]) ).
tcf(c_4217,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_3350,c_114]) ).
tcf(c_4234,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,relation_dom(relation_inverse(X2)))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_78]) ).
tcf(c_4235,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_78]) ).
tcf(c_4236,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(sK2))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(light_normalisation,[status(thm)],[c_4235,c_4030]) ).
tcf(c_4237,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(sK2))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4236,c_3611]) ).
tcf(c_4256,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_inverse(X2)))
| ~ relation(X2)
| ~ relation(relation_inverse(X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_296,c_106]) ).
tcf(c_4257,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_106]) ).
tcf(c_4258,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(light_normalisation,[status(thm)],[c_4257,c_3821]) ).
tcf(c_4259,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK1))
| ~ in(ordered_pair(X0,X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4258,c_3611]) ).
tcf(c_4272,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),relation_inverse(empty_set))
| ~ relation(relation_inverse(empty_set))
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_3634,c_297]) ).
tcf(c_4273,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),empty_set)
| ~ relation(relation_inverse(empty_set))
| ~ in(ordered_pair(X0,X1),relation_inverse(empty_set)) ),
inference(superposition,[status(thm)],[c_3634,c_296]) ).
tcf(c_4285,plain,
( empty(relation_inverse(empty_set))
| ~ empty(empty_set)
| ~ relation(relation_inverse(empty_set)) ),
inference(superposition,[status(thm)],[c_3819,c_75]) ).
tcf(c_4289,plain,
( empty(relation_inverse(empty_set))
| ~ relation(relation_inverse(empty_set)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4285,c_136]) ).
tcf(c_4301,plain,
( empty(relation_inverse(empty_set))
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_4311,plain,
( relation(relation_rng(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_121,c_3996]) ).
tcf(c_4318,plain,
( empty(relation_rng(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_121,c_3997]) ).
tcf(c_4321,plain,
( function(relation_dom(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4015,c_4013]) ).
tcf(c_4329,plain,
( relation(relation_dom(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4016,c_4013]) ).
tcf(c_4337,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4017,c_4013]) ).
tcf(c_4345,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4024,c_4013]) ).
tcf(c_4352,plain,
( empty(relation_inverse(sK1))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_73,c_4345]) ).
tcf(c_4363,plain,
( function(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_121,c_4106]) ).
tcf(c_4366,plain,
( empty(relation_inverse(sK9))
| ~ empty(relation_rng(sK9))
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_75]) ).
tcf(c_4367,plain,
( function(relation_rng(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_3208]) ).
tcf(c_4368,plain,
( relation(relation_rng(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_74]) ).
tcf(c_4369,plain,
( empty(relation_rng(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_73]) ).
tcf(c_4385,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(X0,ordered_pair(X1,sK7(X0,X1))) ),
inference(superposition,[status(thm)],[c_79,c_70]) ).
tcf(c_4386,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK7(X1,X0)),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_79,c_69]) ).
tcf(c_4387,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_79,c_67]) ).
tcf(c_4388,plain,
! [X0: $i,X1: $i] :
( in(sK7(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_79,c_106]) ).
tcf(c_4390,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,X0) = sK7(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_79,c_197]) ).
tcf(c_4391,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK7(relation_inverse(X1),X0),X0),X1)
| ~ relation(X1)
| ~ relation(relation_inverse(X1))
| ~ in(X0,relation_dom(relation_inverse(X1))) ),
inference(superposition,[status(thm)],[c_79,c_297]) ).
tcf(c_4392,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_79,c_3784]) ).
tcf(c_4393,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_3719]) ).
tcf(c_4406,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 )
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4392,c_64]) ).
tcf(c_4409,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4393,c_4030]) ).
tcf(c_4410,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4409,c_3611]) ).
tcf(c_4446,plain,
! [X0: $i,X1: $i] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| ~ in(X0,ordered_pair(sK15(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_107,c_70]) ).
tcf(c_4447,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK15(X1,X0),X0),X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_107,c_69]) ).
tcf(c_4448,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_107,c_67]) ).
tcf(c_4450,plain,
! [X0: $i,X1: $i] :
( in(sK15(X1,X0),relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_107,c_78]) ).
tcf(c_4451,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK15(X1,X0)) = X0 )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_107,c_197]) ).
tcf(c_4452,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(X1),X0)),X1)
| ~ relation(X1)
| ~ relation(relation_inverse(X1))
| ~ in(X0,relation_rng(relation_inverse(X1))) ),
inference(superposition,[status(thm)],[c_107,c_297]) ).
tcf(c_4453,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ~ relation(sK1)
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_107,c_3784]) ).
tcf(c_4454,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK1),X0)),sK1)
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_3719]) ).
tcf(c_4467,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4453,c_4013]) ).
tcf(c_4468,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4467,c_64]) ).
tcf(c_4471,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK1),X0)),sK1)
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4454,c_3821]) ).
tcf(c_4472,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK1),X0)),sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4471,c_3611]) ).
tcf(c_4508,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4030,c_89]) ).
tcf(c_4509,plain,
! [X0: $i] :
( in(X0,empty_set)
| ( apply(empty_set,X0) = empty_set )
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_3404,c_89]) ).
tcf(c_4510,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( apply(relation_inverse(sK2),X0) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_89]) ).
tcf(c_4511,plain,
! [X0: $i] :
( in(X0,relation_rng(sK9))
| ( apply(relation_inverse(sK9),X0) = empty_set )
| ~ function(relation_inverse(sK9))
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_89]) ).
tcf(c_4512,plain,
! [X0: $i] :
( in(X0,empty_set)
| ( apply(relation_inverse(empty_set),X0) = empty_set )
| ~ function(relation_inverse(empty_set))
| ~ relation(relation_inverse(empty_set)) ),
inference(superposition,[status(thm)],[c_3819,c_89]) ).
tcf(c_4513,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ in(relation_dom(X0),X1) ),
inference(superposition,[status(thm)],[c_89,c_70]) ).
tcf(c_4514,plain,
! [X0: $i,X1: $i] :
( element(X1,relation_dom(X0))
| ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_69]) ).
tcf(c_4515,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_89,c_67]) ).
tcf(c_4516,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,relation_rng(relation_dom(X0)))
| ( apply(X0,ordered_pair(X1,X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_89,c_106]) ).
tcf(c_4517,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_89,c_78]) ).
tcf(c_4518,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_89,c_197]) ).
tcf(c_4519,plain,
! [X0: $i] :
( in(X0,empty_set)
| ( apply(empty_set,X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4509,c_3172,c_135]) ).
tcf(c_4546,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4508,c_987,c_3611]) ).
tcf(c_4593,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4169,c_87]) ).
tcf(c_4594,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_87,c_70]) ).
tcf(c_4595,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_87,c_69]) ).
tcf(c_4596,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_87,c_67]) ).
tcf(c_4597,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(superposition,[status(thm)],[c_87,c_106]) ).
tcf(c_4600,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(apply(relation_inverse(X1),X0),X0),X1)
| ~ relation(X1)
| ~ function(relation_inverse(X1))
| ~ relation(relation_inverse(X1))
| ~ in(X0,relation_dom(relation_inverse(X1))) ),
inference(superposition,[status(thm)],[c_87,c_297]) ).
tcf(c_4601,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_87,c_3784]) ).
tcf(c_4602,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_3719]) ).
tcf(c_4619,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 )
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4601,c_65,c_64]) ).
tcf(c_4622,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4602,c_4030]) ).
tcf(c_4623,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4622,c_987,c_3611]) ).
tcf(c_4631,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4593,c_65,c_64]) ).
tcf(c_4665,plain,
( ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4120,c_72]) ).
tcf(c_4666,plain,
( ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4120,c_71]) ).
tcf(c_4667,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4120,c_120]) ).
tcf(c_4687,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4121,c_66]) ).
tcf(c_4688,plain,
( ( relation_rng(relation_dom(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3330]) ).
tcf(c_4689,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3327]) ).
tcf(c_4690,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_133]) ).
tcf(c_4693,plain,
( empty(sK2)
| ~ empty(sK1)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_4121,c_75]) ).
tcf(c_4694,plain,
( empty(relation_inverse(sK1))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_4345]) ).
tcf(c_4698,plain,
( empty(sK2)
| ~ empty(sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4693,c_61]) ).
tcf(c_4719,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_4406]) ).
tcf(c_4720,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) = ordered_pair(X0,sK7(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_4406]) ).
tcf(c_4721,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) = ordered_pair(X0,apply(relation_dom(sK1),X0)) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_4406]) ).
tcf(c_4722,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) = ordered_pair(sK15(relation_dom(sK1),X0),X0) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_4406]) ).
tcf(c_4723,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_3448,c_4406]) ).
tcf(c_4726,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4719,c_65,c_64]) ).
tcf(c_4756,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_4468]) ).
tcf(c_4757,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),ordered_pair(X0,sK7(relation_dom(sK2),X0))) = sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_4468]) ).
tcf(c_4758,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),ordered_pair(X0,apply(relation_dom(sK2),X0))) = sK15(sK1,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_87,c_4468]) ).
tcf(c_4759,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),ordered_pair(sK15(relation_dom(sK2),X0),X0)) = sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_4468]) ).
tcf(c_4760,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_3448,c_4468]) ).
tcf(c_4763,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4756,c_62,c_61]) ).
tcf(c_4784,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_4619]) ).
tcf(c_4785,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) = ordered_pair(X0,sK7(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_4619]) ).
tcf(c_4786,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) = ordered_pair(X0,apply(relation_dom(sK1),X0)) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_4619]) ).
tcf(c_4787,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) = ordered_pair(sK15(relation_dom(sK1),X0),X0) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_4619]) ).
tcf(c_4788,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_3448,c_4619]) ).
tcf(c_4791,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4784,c_65,c_64]) ).
tcf(c_4822,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_4726,c_87]) ).
tcf(c_4826,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4822,c_4030]) ).
tcf(c_4827,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4826,c_987,c_3611]) ).
tcf(c_4839,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_4763,c_87]) ).
tcf(c_4840,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,sK7(sK1,X0)) = X0 )
| ( apply(sK2,sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4763,c_4726]) ).
tcf(c_4847,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4839,c_4030]) ).
tcf(c_4848,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4847,c_987,c_3611]) ).
tcf(c_4860,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4169,c_4791]) ).
tcf(c_4862,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_4791,c_87]) ).
tcf(c_4863,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,apply(sK1,X0)) = X0 )
| ( apply(sK2,apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4791,c_4763]) ).
tcf(c_4870,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_4862,c_4030]) ).
tcf(c_4871,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4870,c_987,c_3611]) ).
tcf(c_4899,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_4631,c_70]) ).
tcf(c_4900,plain,
( element(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4631,c_69]) ).
tcf(c_4902,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4631,c_106]) ).
tcf(c_4905,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4631,c_3784]) ).
tcf(c_4906,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4902,c_4013]) ).
tcf(c_4907,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4906,c_64]) ).
tcf(c_4924,plain,
! [X0: $i] :
( in(X0,relation_rng(sK10))
| ( apply(relation_inverse(sK10),X0) = empty_set )
| ~ function(relation_inverse(sK10))
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_89]) ).
tcf(c_4925,plain,
( empty(relation_inverse(sK10))
| ~ empty(relation_rng(sK10))
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_75]) ).
tcf(c_4929,plain,
( ~ empty(relation_rng(sK10))
| ~ relation(relation_inverse(sK10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4925,c_3955]) ).
tcf(c_5065,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ( apply(X0,ordered_pair(sK5(relation_dom(X0),X1),X2)) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_dom(X0))
| ~ in(sK5(relation_dom(X0),X1),X1) ),
inference(superposition,[status(thm)],[c_89,c_76]) ).
tcf(c_5066,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_79,c_76]) ).
tcf(c_5067,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X0) = X1 )
| ~ function(X0)
| ~ relation(X0)
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_87,c_76]) ).
tcf(c_5068,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_dom(relation_inverse(X1)) = X2 )
| ~ relation(X1)
| ~ relation(relation_inverse(X1))
| ~ in(sK5(relation_inverse(X1),X2),X2)
| ~ in(ordered_pair(X0,sK5(relation_inverse(X1),X2)),X1) ),
inference(superposition,[status(thm)],[c_296,c_76]) ).
tcf(c_5069,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK1)) = X1 )
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(relation_inverse(sK1),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK1),X1)),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_76]) ).
tcf(c_5079,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = X1 )
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(relation_inverse(sK1),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK1),X1)),sK1) ),
inference(light_normalisation,[status(thm)],[c_5069,c_4030]) ).
tcf(c_5080,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = X1 )
| ~ in(sK5(relation_inverse(sK1),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK1),X1)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5079,c_3611]) ).
tcf(c_5108,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK5(X0,X1),sK6(X0,X1))) ),
inference(superposition,[status(thm)],[c_77,c_70]) ).
tcf(c_5109,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| element(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_77,c_69]) ).
tcf(c_5110,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_77,c_67]) ).
tcf(c_5112,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(sK6(X0,X1),relation_rng(X0))
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_77,c_106]) ).
tcf(c_5113,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),relation_dom(X0))
| ( relation_dom(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_77,c_78]) ).
tcf(c_5114,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| ( relation_dom(X0) = X1 )
| ( apply(X0,sK5(X0,X1)) = sK6(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_77,c_197]) ).
tcf(c_5115,plain,
! [X0: $i,X1: $i] :
( in(sK5(relation_inverse(X0),X1),X1)
| in(ordered_pair(sK6(relation_inverse(X0),X1),sK5(relation_inverse(X0),X1)),X0)
| ( relation_dom(relation_inverse(X0)) = X1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_77,c_297]) ).
tcf(c_5116,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) = ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_4619]) ).
tcf(c_5117,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) = ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_4406]) ).
tcf(c_5118,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_77,c_3784]) ).
tcf(c_5119,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK1),X0),sK5(relation_inverse(sK1),X0)),sK1)
| ( relation_dom(relation_inverse(sK1)) = X0 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_3719]) ).
tcf(c_5120,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) = sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_4468]) ).
tcf(c_5141,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5118,c_64]) ).
tcf(c_5150,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK1),X0),sK5(relation_inverse(sK1),X0)),sK1)
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_5119,c_4030]) ).
tcf(c_5151,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK1),X0),sK5(relation_inverse(sK1),X0)),sK1)
| ( relation_dom(sK2) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5150,c_3611]) ).
tcf(c_5187,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_66]) ).
tcf(c_5188,plain,
( ( relation_rng(relation_inverse(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3330]) ).
tcf(c_5189,plain,
( ( relation_dom(relation_inverse(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3327]) ).
tcf(c_5190,plain,
( ( relation_inverse(sK1) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_133]) ).
tcf(c_5193,plain,
( empty(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_4337]) ).
tcf(c_5194,plain,
( relation(relation_dom(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_4329]) ).
tcf(c_5203,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_5189,c_4030]) ).
tcf(c_5206,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_5188,c_3821]) ).
tcf(c_5246,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) )
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5141,c_70]) ).
tcf(c_5247,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5141,c_69]) ).
tcf(c_5248,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_67]) ).
tcf(c_5251,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5141,c_4468]) ).
tcf(c_5274,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_4907]) ).
tcf(c_5275,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5274,c_65,c_64]) ).
tcf(c_5288,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(relation_dom(sK2),sK20(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_5275,c_70]) ).
tcf(c_5289,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5275,c_69]) ).
tcf(c_5290,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5275,c_67]) ).
tcf(c_5291,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5275,c_4468]) ).
tcf(c_5323,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_77,c_4237]) ).
tcf(c_5324,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_79,c_4237]) ).
tcf(c_5325,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_87,c_4237]) ).
tcf(c_5326,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ~ relation(sK1)
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_107,c_4237]) ).
tcf(c_5329,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5324,c_64]) ).
tcf(c_5332,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5325,c_65,c_64]) ).
tcf(c_5335,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5323,c_64]) ).
tcf(c_5346,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5329,c_70]) ).
tcf(c_5347,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_69]) ).
tcf(c_5348,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_67]) ).
tcf(c_5349,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_4468]) ).
tcf(c_5364,plain,
relation_rng(sK1) = relation_dom(sK2),
inference(global_subsumption_just,[status(thm)],[c_1713,c_4013]) ).
tcf(c_5366,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_1784,c_5364]) ).
tcf(c_5376,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,X0)) = X0 )
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_1810,c_5364]) ).
tcf(c_5406,plain,
! [X0: $i] :
( in(X0,relation_rng(sK12))
| ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_89]) ).
tcf(c_5407,plain,
( empty(relation_inverse(sK12))
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_75]) ).
tcf(c_5408,plain,
( function(relation_rng(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_3208]) ).
tcf(c_5409,plain,
( relation(relation_rng(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_74]) ).
tcf(c_5410,plain,
( empty(relation_rng(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_73]) ).
tcf(c_5417,plain,
( empty(relation_inverse(sK12))
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5407,c_3610]) ).
tcf(c_5420,plain,
! [X0: $i] :
( in(X0,relation_rng(sK12))
| ( apply(relation_inverse(sK12),X0) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5406,c_1001,c_3610]) ).
tcf(c_5442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_dom(X0)) = X1 )
| ( apply(X0,ordered_pair(X2,sK13(relation_dom(X0),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_dom(X0))
| ~ in(sK13(relation_dom(X0),X1),X1) ),
inference(superposition,[status(thm)],[c_89,c_104]) ).
tcf(c_5443,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(X0) = X1 )
| ~ relation(X0)
| ~ in(sK13(X0,X1),X1)
| ~ in(sK13(X0,X1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_107,c_104]) ).
tcf(c_5444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( relation_rng(relation_inverse(X0)) = X1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(sK13(relation_inverse(X0),X1),X1)
| ~ in(ordered_pair(sK13(relation_inverse(X0),X1),X2),X0) ),
inference(superposition,[status(thm)],[c_296,c_104]) ).
tcf(c_5445,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK1)) = X0 )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK1),X0),X1),sK1) ),
inference(superposition,[status(thm)],[c_3722,c_104]) ).
tcf(c_5450,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1) = X0 )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK1),X0),X1),sK1) ),
inference(light_normalisation,[status(thm)],[c_5445,c_3821]) ).
tcf(c_5451,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1) = X0 )
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK1),X0),X1),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5450,c_3611]) ).
tcf(c_5523,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| ( relation_rng(X0) = X1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK14(X0,X1),sK13(X0,X1))) ),
inference(superposition,[status(thm)],[c_105,c_70]) ).
tcf(c_5524,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| element(ordered_pair(sK14(X0,X1),sK13(X0,X1)),X0)
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_69]) ).
tcf(c_5525,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| ( relation_rng(X0) = X1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_67]) ).
tcf(c_5526,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| in(sK13(X0,X1),relation_rng(X0))
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_106]) ).
tcf(c_5527,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| in(sK14(X0,X1),relation_dom(X0))
| ( relation_rng(X0) = X1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_78]) ).
tcf(c_5528,plain,
! [X0: $i,X1: $i] :
( in(sK13(X0,X1),X1)
| ( relation_rng(X0) = X1 )
| ( apply(X0,sK14(X0,X1)) = sK13(X0,X1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_105,c_197]) ).
tcf(c_5530,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_inverse(X0),X1),X1)
| in(ordered_pair(sK13(relation_inverse(X0),X1),sK14(relation_inverse(X0),X1)),X0)
| ( relation_rng(relation_inverse(X0)) = X1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_105,c_297]) ).
tcf(c_5531,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) = ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_4619]) ).
tcf(c_5532,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) = ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_4406]) ).
tcf(c_5533,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_rng(sK1) = X0 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_105,c_4237]) ).
tcf(c_5534,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_rng(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_105,c_3784]) ).
tcf(c_5535,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK1),X0),sK14(relation_inverse(sK1),X0)),sK1)
| ( relation_rng(relation_inverse(sK1)) = X0 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_3719]) ).
tcf(c_5536,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) = sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_4468]) ).
tcf(c_5541,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_5533,c_4013]) ).
tcf(c_5542,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5541,c_64]) ).
tcf(c_5562,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) )
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_5534,c_4013]) ).
tcf(c_5563,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5562,c_64]) ).
tcf(c_5572,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK1),X0),sK14(relation_inverse(sK1),X0)),sK1)
| ( relation_dom(sK1) = X0 )
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_5535,c_3821]) ).
tcf(c_5573,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK1),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK1),X0),sK14(relation_inverse(sK1),X0)),sK1)
| ( relation_dom(sK1) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5572,c_3611]) ).
tcf(c_5616,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,X0),sK24(X1,X0)),X1)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(X1,X0),sK24(X1,X0))) ),
inference(superposition,[status(thm)],[c_130,c_70]) ).
tcf(c_5617,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_69]) ).
tcf(c_5618,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67]) ).
tcf(c_5619,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),relation_rng(X1))
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_106]) ).
tcf(c_5620,plain,
! [X0: $i,X1: $i] :
( in(sK23(X0,X1),relation_dom(X1))
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_78]) ).
tcf(c_5621,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| ( X0 = X1 )
| ( apply(X1,sK23(X0,X1)) = sK24(X0,X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_197]) ).
tcf(c_5622,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK24(X1,relation_inverse(X0)),sK23(X1,relation_inverse(X0))),X0)
| in(ordered_pair(sK23(X1,relation_inverse(X0)),sK24(X1,relation_inverse(X0))),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_130,c_297]) ).
tcf(c_5623,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4619]) ).
tcf(c_5624,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4406]) ).
tcf(c_5625,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_4237]) ).
tcf(c_5626,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_3784]) ).
tcf(c_5627,plain,
! [X0: $i] :
( in(ordered_pair(sK24(X0,relation_inverse(sK1)),sK23(X0,relation_inverse(sK1))),sK1)
| in(ordered_pair(sK23(X0,relation_inverse(sK1)),sK24(X0,relation_inverse(sK1))),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_3719]) ).
tcf(c_5628,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_4468]) ).
tcf(c_5629,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(X0,X1),sK24(X0,X1))) ),
inference(superposition,[status(thm)],[c_130,c_70]) ).
tcf(c_5630,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X0)
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_69]) ).
tcf(c_5631,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67]) ).
tcf(c_5632,plain,
! [X0: $i,X1: $i] :
( in(sK24(X0,X1),relation_rng(X0))
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_106]) ).
tcf(c_5633,plain,
! [X0: $i,X1: $i] :
( in(sK23(X0,X1),relation_dom(X0))
| in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_78]) ).
tcf(c_5634,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X0,X1),sK24(X0,X1)),X1)
| ( X0 = X1 )
| ( apply(X0,sK23(X0,X1)) = sK24(X0,X1) )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_197]) ).
tcf(c_5635,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK24(relation_inverse(X0),X1),sK23(relation_inverse(X0),X1)),X0)
| in(ordered_pair(sK23(relation_inverse(X0),X1),sK24(relation_inverse(X0),X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_130,c_297]) ).
tcf(c_5636,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) = ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4619]) ).
tcf(c_5637,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) = ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4406]) ).
tcf(c_5638,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_4237]) ).
tcf(c_5639,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_3784]) ).
tcf(c_5640,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(sK1),X0),sK23(relation_inverse(sK1),X0)),sK1)
| in(ordered_pair(sK23(relation_inverse(sK1),X0),sK24(relation_inverse(sK1),X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_3719]) ).
tcf(c_5641,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_4468]) ).
tcf(c_5654,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5638,c_64]) ).
tcf(c_5669,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5625,c_64]) ).
tcf(c_5704,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5639,c_64]) ).
tcf(c_5709,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5626,c_64]) ).
tcf(c_5726,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(sK1),X0),sK23(relation_inverse(sK1),X0)),sK1)
| in(ordered_pair(sK23(relation_inverse(sK1),X0),sK24(relation_inverse(sK1),X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5640,c_3611]) ).
tcf(c_5731,plain,
! [X0: $i] :
( in(ordered_pair(sK24(X0,relation_inverse(sK1)),sK23(X0,relation_inverse(sK1))),sK1)
| in(ordered_pair(sK23(X0,relation_inverse(sK1)),sK24(X0,relation_inverse(sK1))),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5627,c_3611]) ).
tcf(c_5793,plain,
! [X0: $i] :
( empty(relation_dom(X0))
| ~ empty(empty_set)
| ( relation_dom(X0) != empty_set ) ),
inference(instantiation,[status(thm)],[c_3991]) ).
tcf(c_5796,plain,
( empty(relation_dom(sK1))
| ~ empty(empty_set)
| ( relation_dom(sK1) != empty_set ) ),
inference(instantiation,[status(thm)],[c_5793]) ).
tcf(c_5808,plain,
! [X0: $i] :
( empty(relation_inverse(X0))
| ~ empty(empty_set)
| ( relation_inverse(X0) != empty_set ) ),
inference(instantiation,[status(thm)],[c_3991]) ).
tcf(c_5811,plain,
( empty(relation_inverse(sK1))
| ~ empty(empty_set)
| ( relation_inverse(sK1) != empty_set ) ),
inference(instantiation,[status(thm)],[c_5808]) ).
tcf(c_5878,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,X0),sK21(X1,X0)),X1)
| ( relation_inverse(X1) = X0 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK21(X1,X0),sK22(X1,X0))) ),
inference(superposition,[status(thm)],[c_125,c_70]) ).
tcf(c_5879,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_69]) ).
tcf(c_5880,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ~ empty(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67]) ).
tcf(c_5881,plain,
! [X0: $i,X1: $i] :
( in(sK22(X0,X1),relation_rng(X1))
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_106]) ).
tcf(c_5882,plain,
! [X0: $i,X1: $i] :
( in(sK21(X0,X1),relation_dom(X1))
| in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_78]) ).
tcf(c_5883,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| ( relation_inverse(X0) = X1 )
| ( apply(X1,sK21(X0,X1)) = sK22(X0,X1) )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_197]) ).
tcf(c_5884,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,relation_inverse(X0)),sK21(X1,relation_inverse(X0))),X1)
| in(ordered_pair(sK22(X1,relation_inverse(X0)),sK21(X1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(X1) )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_125,c_297]) ).
tcf(c_5885,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) = ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4619]) ).
tcf(c_5886,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) = ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4406]) ).
tcf(c_5887,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_4237]) ).
tcf(c_5888,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_3784]) ).
tcf(c_5889,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_inverse(sK1)),sK21(X0,relation_inverse(sK1))),sK1)
| in(ordered_pair(sK22(X0,relation_inverse(sK1)),sK21(X0,relation_inverse(sK1))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_3719]) ).
tcf(c_5890,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_4468]) ).
tcf(c_5891,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK22(X0,X1),sK21(X0,X1))) ),
inference(superposition,[status(thm)],[c_125,c_70]) ).
tcf(c_5892,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK22(X0,X1),sK21(X0,X1)),X0)
| in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_69]) ).
tcf(c_5893,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67]) ).
tcf(c_5894,plain,
! [X0: $i,X1: $i] :
( in(sK21(X0,X1),relation_rng(X0))
| in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_106]) ).
tcf(c_5895,plain,
! [X0: $i,X1: $i] :
( in(sK22(X0,X1),relation_dom(X0))
| in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_78]) ).
tcf(c_5896,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X1)
| ( relation_inverse(X0) = X1 )
| ( apply(X0,sK22(X0,X1)) = sK21(X0,X1) )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_197]) ).
tcf(c_5897,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(relation_inverse(X0),X1),sK22(relation_inverse(X0),X1)),X1)
| in(ordered_pair(sK21(relation_inverse(X0),X1),sK22(relation_inverse(X0),X1)),X0)
| ( relation_inverse(relation_inverse(X0)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_125,c_297]) ).
tcf(c_5898,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4619]) ).
tcf(c_5899,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4406]) ).
tcf(c_5900,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_4237]) ).
tcf(c_5901,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_3784]) ).
tcf(c_5902,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0)
| ( relation_inverse(relation_inverse(sK1)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_3719]) ).
tcf(c_5903,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_4468]) ).
tcf(c_5914,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5900,c_64]) ).
tcf(c_5929,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5887,c_64]) ).
tcf(c_5964,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5901,c_64]) ).
tcf(c_5969,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5888,c_64]) ).
tcf(c_5986,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_5902,c_3625]) ).
tcf(c_5987,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5986,c_3611]) ).
tcf(c_5992,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_inverse(sK1)),sK21(X0,relation_inverse(sK1))),sK1)
| in(ordered_pair(sK22(X0,relation_inverse(sK1)),sK21(X0,relation_inverse(sK1))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5889,c_3611]) ).
tcf(c_6132,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5366,c_67]) ).
tcf(c_6246,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5332,c_70]) ).
tcf(c_6247,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_69]) ).
tcf(c_6249,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_4468]) ).
tcf(c_6279,plain,
! [X0: $i] :
( in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5335,c_70]) ).
tcf(c_6280,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_5335,c_69]) ).
tcf(c_6281,plain,
! [X0: $i] :
( in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_67]) ).
tcf(c_6284,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5335,c_4468]) ).
tcf(c_6285,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ in(relation_dom(sK2),sK6(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5335,c_70]) ).
tcf(c_6286,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_5335,c_69]) ).
tcf(c_6287,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_67]) ).
tcf(c_6288,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5335,c_4468]) ).
tcf(c_6329,plain,
! [X0: $i] :
( in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5542,c_70]) ).
tcf(c_6330,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_5542,c_69]) ).
tcf(c_6331,plain,
! [X0: $i] :
( in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_67]) ).
tcf(c_6332,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5542,c_4619]) ).
tcf(c_6333,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5542,c_4406]) ).
tcf(c_6335,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ in(relation_dom(sK2),sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5542,c_70]) ).
tcf(c_6336,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_5542,c_69]) ).
tcf(c_6337,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_67]) ).
tcf(c_6338,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5542,c_4468]) ).
tcf(c_6402,plain,
! [X0: $i] :
( empty(X0)
| in(sK20(X0),X0) ),
inference(superposition,[status(thm)],[c_119,c_68]) ).
tcf(c_6417,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) )
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_5563,c_70]) ).
tcf(c_6418,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5563,c_69]) ).
tcf(c_6419,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_67]) ).
tcf(c_6420,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5563,c_4619]) ).
tcf(c_6421,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5563,c_4406]) ).
tcf(c_6471,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(sK1,X0),sK24(sK1,X0))) ),
inference(superposition,[status(thm)],[c_5654,c_70]) ).
tcf(c_6472,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| element(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5654,c_69]) ).
tcf(c_6473,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5654,c_67]) ).
tcf(c_6474,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| in(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5654,c_106]) ).
tcf(c_6475,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5654,c_78]) ).
tcf(c_6476,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ( apply(X0,sK23(sK1,X0)) = sK24(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5654,c_197]) ).
tcf(c_6477,plain,
! [X0: $i] :
( in(sK24(sK1,relation_inverse(X0)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(X0)),sK23(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5654,c_297]) ).
tcf(c_6478,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_4619]) ).
tcf(c_6479,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_4406]) ).
tcf(c_6482,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_3719]) ).
tcf(c_6483,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_4468]) ).
tcf(c_6509,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6482,c_3611]) ).
tcf(c_6561,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(X0,sK1),sK24(X0,sK1))) ),
inference(superposition,[status(thm)],[c_5669,c_70]) ).
tcf(c_6562,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| element(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5669,c_69]) ).
tcf(c_6563,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5669,c_67]) ).
tcf(c_6564,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| in(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5669,c_106]) ).
tcf(c_6565,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5669,c_78]) ).
tcf(c_6566,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ( apply(X0,sK23(X0,sK1)) = sK24(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5669,c_197]) ).
tcf(c_6567,plain,
! [X0: $i] :
( in(sK24(relation_inverse(X0),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(X0),sK1),sK23(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5669,c_297]) ).
tcf(c_6568,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_4619]) ).
tcf(c_6569,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_4406]) ).
tcf(c_6572,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_3719]) ).
tcf(c_6573,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_4468]) ).
tcf(c_6599,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6572,c_3611]) ).
tcf(c_6636,plain,
( empty(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6402,c_5376]) ).
tcf(c_6669,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK21(sK1,X0),sK22(sK1,X0))) ),
inference(superposition,[status(thm)],[c_5914,c_70]) ).
tcf(c_6670,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| element(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5914,c_69]) ).
tcf(c_6671,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5914,c_67]) ).
tcf(c_6672,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5914,c_106]) ).
tcf(c_6673,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5914,c_78]) ).
tcf(c_6674,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ( apply(X0,sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5914,c_197]) ).
tcf(c_6675,plain,
! [X0: $i] :
( in(sK21(sK1,relation_inverse(X0)),relation_dom(sK2))
| in(ordered_pair(sK22(sK1,relation_inverse(X0)),sK21(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5914,c_297]) ).
tcf(c_6676,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_4619]) ).
tcf(c_6677,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_4406]) ).
tcf(c_6678,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5914,c_4237]) ).
tcf(c_6679,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5914,c_3784]) ).
tcf(c_6681,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_4468]) ).
tcf(c_6686,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6678,c_64]) ).
tcf(c_6706,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6679,c_64]) ).
tcf(c_6777,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_6686,c_70]) ).
tcf(c_6778,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_6686,c_69]) ).
tcf(c_6779,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6686,c_67]) ).
tcf(c_6780,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_6686,c_4468]) ).
tcf(c_6800,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6636,c_133]) ).
tcf(c_6803,plain,
( empty(sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6636,c_75]) ).
tcf(c_6814,plain,
( empty(sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6803,c_61]) ).
tcf(c_6824,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(light_normalisation,[status(thm)],[c_3817,c_4013]) ).
tcf(c_6837,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6824,c_87]) ).
tcf(c_6838,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6824,c_5332]) ).
tcf(c_6839,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6824,c_4791]) ).
tcf(c_6852,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6837,c_65,c_64]) ).
tcf(c_6881,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(X1) = X0 )
| ( apply(X1,ordered_pair(sK23(X0,relation_dom(X1)),sK24(X0,relation_dom(X1)))) = empty_set )
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(X1))
| ~ in(ordered_pair(sK23(X0,relation_dom(X1)),sK24(X0,relation_dom(X1))),X0) ),
inference(superposition,[status(thm)],[c_89,c_129]) ).
tcf(c_6882,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(X1) = X0 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X1))
| ~ in(ordered_pair(sK24(X0,relation_inverse(X1)),sK23(X0,relation_inverse(X1))),X1)
| ~ in(ordered_pair(sK23(X0,relation_inverse(X1)),sK24(X0,relation_inverse(X1))),X0) ),
inference(superposition,[status(thm)],[c_296,c_129]) ).
tcf(c_6885,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(sK24(X0,relation_inverse(sK1)),sK23(X0,relation_inverse(sK1))),sK1)
| ~ in(ordered_pair(sK23(X0,relation_inverse(sK1)),sK24(X0,relation_inverse(sK1))),X0) ),
inference(superposition,[status(thm)],[c_3722,c_129]) ).
tcf(c_6887,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(superposition,[status(thm)],[c_5654,c_129]) ).
tcf(c_6888,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6887,c_64]) ).
tcf(c_6893,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(ordered_pair(sK24(X0,relation_inverse(sK1)),sK23(X0,relation_inverse(sK1))),sK1)
| ~ in(ordered_pair(sK23(X0,relation_inverse(sK1)),sK24(X0,relation_inverse(sK1))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6885,c_3611]) ).
tcf(c_6938,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(X0)) = X1 )
| ( apply(X0,ordered_pair(sK22(relation_dom(X0),X1),sK21(relation_dom(X0),X1))) = empty_set )
| ~ function(X0)
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_dom(X0))
| ~ in(ordered_pair(sK21(relation_dom(X0),X1),sK22(relation_dom(X0),X1)),X1) ),
inference(superposition,[status(thm)],[c_89,c_124]) ).
tcf(c_6940,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(X0)) = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ relation(relation_inverse(X0))
| ~ in(ordered_pair(sK21(relation_inverse(X0),X1),sK22(relation_inverse(X0),X1)),X1)
| ~ in(ordered_pair(sK21(relation_inverse(X0),X1),sK22(relation_inverse(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_296,c_124]) ).
tcf(c_6941,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK1)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0) ),
inference(superposition,[status(thm)],[c_3722,c_124]) ).
tcf(c_6942,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK1))
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0) ),
inference(light_normalisation,[status(thm)],[c_6941,c_3625]) ).
tcf(c_6943,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(X0)
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),sK1)
| ~ in(ordered_pair(sK21(relation_inverse(sK1),X0),sK22(relation_inverse(sK1),X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6942,c_3611]) ).
tcf(c_6975,plain,
( empty(relation_inverse(sK12))
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_103]) ).
tcf(c_6976,plain,
( function(relation_dom(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_3221]) ).
tcf(c_6977,plain,
( relation(relation_dom(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_102]) ).
tcf(c_6978,plain,
( empty(relation_dom(sK12))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_101]) ).
tcf(c_6985,plain,
( empty(relation_inverse(sK12))
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6975,c_3610]) ).
tcf(c_7007,plain,
( empty(relation_inverse(sK9))
| ~ empty(relation_dom(sK9))
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_103]) ).
tcf(c_7008,plain,
( function(relation_dom(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_3221]) ).
tcf(c_7009,plain,
( relation(relation_dom(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_102]) ).
tcf(c_7010,plain,
( empty(relation_dom(sK9))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_101]) ).
tcf(c_7029,plain,
( empty(relation_inverse(sK10))
| ~ empty(relation_dom(sK10))
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_103]) ).
tcf(c_7033,plain,
( ~ empty(relation_dom(sK10))
| ~ relation(relation_inverse(sK10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7029,c_3955]) ).
tcf(c_7045,plain,
( function(relation_dom(sK1))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_4145]) ).
tcf(c_7046,plain,
( function(relation_dom(sK1))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_4145]) ).
tcf(c_7057,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_6706,c_70]) ).
tcf(c_7058,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6706,c_69]) ).
tcf(c_7059,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6706,c_67]) ).
tcf(c_7060,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6706,c_4468]) ).
tcf(c_7103,plain,
( relation(relation_inverse(sK1))
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_980,c_108]) ).
tcf(c_7106,plain,
relation(relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_7103,c_65,c_64]) ).
tcf(c_7115,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK22(X0,sK1),sK21(X0,sK1))) ),
inference(superposition,[status(thm)],[c_5929,c_70]) ).
tcf(c_7116,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| element(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5929,c_69]) ).
tcf(c_7117,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5929,c_67]) ).
tcf(c_7118,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| in(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5929,c_106]) ).
tcf(c_7119,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5929,c_78]) ).
tcf(c_7120,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ( apply(X0,sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5929,c_197]) ).
tcf(c_7121,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_5929,c_124]) ).
tcf(c_7122,plain,
! [X0: $i] :
( in(sK22(relation_inverse(X0),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(X0),sK1),sK22(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5929,c_297]) ).
tcf(c_7123,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_4619]) ).
tcf(c_7124,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_4406]) ).
tcf(c_7126,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5929,c_3784]) ).
tcf(c_7128,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_4468]) ).
tcf(c_7149,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7126,c_64]) ).
tcf(c_7153,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7121,c_64]) ).
tcf(c_7208,plain,
relation_inverse(relation_inverse(sK1)) = sK1,
inference(superposition,[status(thm)],[c_64,c_120]) ).
tcf(c_7238,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_7149,c_70]) ).
tcf(c_7239,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7149,c_69]) ).
tcf(c_7240,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7149,c_67]) ).
tcf(c_7241,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7149,c_4468]) ).
tcf(c_7288,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(sK1,X0),sK24(sK1,X0))) ),
inference(superposition,[status(thm)],[c_5704,c_70]) ).
tcf(c_7289,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5704,c_69]) ).
tcf(c_7290,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5704,c_67]) ).
tcf(c_7291,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5704,c_106]) ).
tcf(c_7292,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5704,c_78]) ).
tcf(c_7293,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(X0,sK23(sK1,X0)) = sK24(sK1,X0) )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5704,c_197]) ).
tcf(c_7294,plain,
! [X0: $i] :
( in(ordered_pair(sK24(sK1,relation_inverse(X0)),sK23(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(X0))) = sK23(sK1,relation_inverse(X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5704,c_297]) ).
tcf(c_7295,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(superposition,[status(thm)],[c_5704,c_129]) ).
tcf(c_7296,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_4619]) ).
tcf(c_7297,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_4406]) ).
tcf(c_7300,plain,
( in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1))) = sK23(sK1,relation_inverse(sK1)) )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_3719]) ).
tcf(c_7301,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_4468]) ).
tcf(c_7322,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK23(sK1,X0) )
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7295,c_64]) ).
tcf(c_7332,plain,
( in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1))) = sK23(sK1,relation_inverse(sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7300,c_3611]) ).
tcf(c_7361,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(X0,sK1),sK24(X0,sK1))) ),
inference(superposition,[status(thm)],[c_5709,c_70]) ).
tcf(c_7362,plain,
! [X0: $i] :
( element(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5709,c_69]) ).
tcf(c_7363,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5709,c_67]) ).
tcf(c_7364,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5709,c_106]) ).
tcf(c_7365,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5709,c_78]) ).
tcf(c_7366,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(X0,sK23(X0,sK1)) = sK24(X0,sK1) )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK23(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5709,c_197]) ).
tcf(c_7367,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(X0),sK1),sK23(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(X0),sK1)) = sK23(relation_inverse(X0),sK1) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5709,c_297]) ).
tcf(c_7369,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_4619]) ).
tcf(c_7370,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_4406]) ).
tcf(c_7373,plain,
( in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1)) = sK23(relation_inverse(sK1),sK1) )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_3719]) ).
tcf(c_7374,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_4468]) ).
tcf(c_7400,plain,
( in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1)) = sK23(relation_inverse(sK1),sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7373,c_3611]) ).
tcf(c_7439,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK21(sK1,X0),sK22(sK1,X0))) ),
inference(superposition,[status(thm)],[c_5964,c_70]) ).
tcf(c_7440,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5964,c_69]) ).
tcf(c_7441,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5964,c_67]) ).
tcf(c_7442,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5964,c_106]) ).
tcf(c_7443,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5964,c_78]) ).
tcf(c_7444,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(X0,sK21(sK1,X0)) = sK22(sK1,X0) )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5964,c_197]) ).
tcf(c_7445,plain,
! [X0: $i] :
( in(ordered_pair(sK22(sK1,relation_inverse(X0)),sK21(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_inverse(X0))) = sK22(sK1,relation_inverse(X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5964,c_297]) ).
tcf(c_7446,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_4619]) ).
tcf(c_7447,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_4406]) ).
tcf(c_7449,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5964,c_3784]) ).
tcf(c_7451,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_4468]) ).
tcf(c_7472,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7449,c_64]) ).
tcf(c_7557,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(light_normalisation,[status(thm)],[c_3857,c_4013]) ).
tcf(c_7570,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7557,c_87]) ).
tcf(c_7571,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7557,c_5332]) ).
tcf(c_7572,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_7557,c_4791]) ).
tcf(c_7585,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7570,c_65,c_64]) ).
tcf(c_7608,plain,
( relation(relation_dom(sK1))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_4146]) ).
tcf(c_7609,plain,
( relation(relation_dom(sK1))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_4146]) ).
tcf(c_7618,plain,
( empty(relation_dom(sK1))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_4147]) ).
tcf(c_7619,plain,
( empty(relation_dom(sK1))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_4147]) ).
tcf(c_7632,plain,
( ( relation_rng(relation_inverse(relation_dom(sK1))) = relation_dom(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7609,c_72]) ).
tcf(c_7633,plain,
( ( relation_dom(relation_inverse(relation_dom(sK1))) = relation_rng(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7609,c_71]) ).
tcf(c_7634,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK1))) = relation_dom(sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7609,c_120]) ).
tcf(c_7652,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6814,c_66]) ).
tcf(c_7685,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7619,c_66]) ).
tcf(c_7686,plain,
( ( relation_rng(relation_dom(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3330]) ).
tcf(c_7687,plain,
( ( relation_dom(relation_dom(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3327]) ).
tcf(c_7711,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_7472,c_87]) ).
tcf(c_7712,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_4763]) ).
tcf(c_7721,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_7711,c_4030]) ).
tcf(c_7722,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7721,c_987,c_3611]) ).
tcf(c_7750,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK22(X0,sK1),sK21(X0,sK1))) ),
inference(superposition,[status(thm)],[c_5969,c_70]) ).
tcf(c_7751,plain,
! [X0: $i] :
( element(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5969,c_69]) ).
tcf(c_7752,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5969,c_67]) ).
tcf(c_7753,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5969,c_106]) ).
tcf(c_7754,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5969,c_78]) ).
tcf(c_7755,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(X0,sK22(X0,sK1)) = sK21(X0,sK1) )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_5969,c_197]) ).
tcf(c_7756,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_5969,c_124]) ).
tcf(c_7757,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(X0),sK1),sK22(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(X0),sK1)) = sK21(relation_inverse(X0),sK1) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_5969,c_297]) ).
tcf(c_7758,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_4619]) ).
tcf(c_7759,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_4406]) ).
tcf(c_7763,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_4468]) ).
tcf(c_7784,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7756,c_64]) ).
tcf(c_7858,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_6852,c_70]) ).
tcf(c_7859,plain,
( element(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6852,c_69]) ).
tcf(c_7861,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6852,c_106]) ).
tcf(c_7865,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6852,c_3784]) ).
tcf(c_7866,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_7861,c_4013]) ).
tcf(c_7888,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_7585,c_70]) ).
tcf(c_7889,plain,
( element(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7585,c_69]) ).
tcf(c_7891,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7585,c_106]) ).
tcf(c_7895,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7585,c_3784]) ).
tcf(c_7896,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_7891,c_4013]) ).
tcf(c_7914,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89,c_5348]) ).
tcf(c_7915,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_5348]) ).
tcf(c_7916,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_5348]) ).
tcf(c_7917,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_5348]) ).
tcf(c_7918,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_5348]) ).
tcf(c_7919,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_5348]) ).
tcf(c_7920,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_5348]) ).
tcf(c_7921,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_5348]) ).
tcf(c_7922,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_5348]) ).
tcf(c_7923,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_5348]) ).
tcf(c_7924,plain,
( empty(relation_dom(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_5348]) ).
tcf(c_7927,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5563,c_5348]) ).
tcf(c_7928,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_5348]) ).
tcf(c_7929,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_5348]) ).
tcf(c_7930,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_5348]) ).
tcf(c_7931,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_5348]) ).
tcf(c_7932,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_5348]) ).
tcf(c_7933,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_5348]) ).
tcf(c_7934,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_5348]) ).
tcf(c_7935,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_5348]) ).
tcf(c_7936,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_5348]) ).
tcf(c_7945,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7914,c_65,c_64]) ).
tcf(c_8078,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_73,c_7945]) ).
tcf(c_8079,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_7945]) ).
tcf(c_8115,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_4202,c_136,c_3966]) ).
tcf(c_8118,plain,
! [X0: $i] :
( in(sK5(empty_set,X0),X0)
| ( relation_dom(empty_set) = X0 )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_77,c_8115]) ).
tcf(c_8119,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_79,c_8115]) ).
tcf(c_8120,plain,
! [X0: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,relation_dom(empty_set)) ),
inference(superposition,[status(thm)],[c_87,c_8115]) ).
tcf(c_8121,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),X0)
| ( relation_rng(empty_set) = X0 )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_105,c_8115]) ).
tcf(c_8122,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,relation_rng(empty_set)) ),
inference(superposition,[status(thm)],[c_107,c_8115]) ).
tcf(c_8123,plain,
! [X0: $i] :
( in(ordered_pair(sK21(empty_set,X0),sK22(empty_set,X0)),X0)
| ( relation_inverse(empty_set) = X0 )
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_8115]) ).
tcf(c_8124,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,empty_set),sK21(X0,empty_set)),X0)
| ( relation_inverse(X0) = empty_set )
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_8115]) ).
tcf(c_8125,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,empty_set),sK24(X0,empty_set)),X0)
| ( X0 = empty_set )
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_8115]) ).
tcf(c_8126,plain,
! [X0: $i] :
( in(ordered_pair(sK23(empty_set,X0),sK24(empty_set,X0)),X0)
| ( X0 = empty_set )
| ~ relation(empty_set)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_8115]) ).
tcf(c_8128,plain,
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK1) = empty_set ) ),
inference(superposition,[status(thm)],[c_5335,c_8115]) ).
tcf(c_8129,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK5(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_5141,c_8115]) ).
tcf(c_8130,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_5563,c_8115]) ).
tcf(c_8131,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_5542,c_8115]) ).
tcf(c_8132,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK23(empty_set,sK1) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5709,c_8115]) ).
tcf(c_8133,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ( sK1 = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5669,c_8115]) ).
tcf(c_8134,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK23(sK1,empty_set) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5704,c_8115]) ).
tcf(c_8135,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ( sK1 = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5654,c_8115]) ).
tcf(c_8136,plain,
( ( relation_inverse(empty_set) = sK1 )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK21(empty_set,sK1) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5969,c_8115]) ).
tcf(c_8137,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ( relation_inverse(empty_set) = sK1 )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5929,c_8115]) ).
tcf(c_8138,plain,
( ( relation_inverse(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5964,c_8115]) ).
tcf(c_8139,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ( relation_inverse(sK1) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_5914,c_8115]) ).
tcf(c_8140,plain,
! [X0: $i] :
( ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_8122,c_3424]) ).
tcf(c_8146,plain,
! [X0: $i] :
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ in(X0,empty_set) ),
inference(light_normalisation,[status(thm)],[c_8120,c_3404]) ).
tcf(c_8147,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8135,c_135]) ).
tcf(c_8150,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8133,c_135]) ).
tcf(c_8153,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),X0)
| ( X0 = empty_set )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8121,c_3424]) ).
tcf(c_8154,plain,
! [X0: $i] :
( in(sK13(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8153,c_135]) ).
tcf(c_8157,plain,
! [X0: $i] :
( in(sK5(empty_set,X0),X0)
| ( X0 = empty_set )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_8118,c_3404]) ).
tcf(c_8158,plain,
! [X0: $i] :
( in(sK5(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8157,c_135]) ).
tcf(c_8161,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ( relation_inverse(sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8139,c_135]) ).
tcf(c_8164,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ( relation_inverse(empty_set) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8137,c_135]) ).
tcf(c_8171,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK23(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8134,c_135]) ).
tcf(c_8174,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK23(empty_set,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8132,c_135]) ).
tcf(c_8177,plain,
( ( relation_inverse(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK22(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8138,c_135]) ).
tcf(c_8180,plain,
( ( relation_inverse(empty_set) = sK1 )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK21(empty_set,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8136,c_135]) ).
tcf(c_8183,plain,
! [X0: $i] :
( in(ordered_pair(sK23(empty_set,X0),sK24(empty_set,X0)),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8126,c_135]) ).
tcf(c_8187,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,empty_set),sK24(X0,empty_set)),X0)
| ( X0 = empty_set )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8125,c_135]) ).
tcf(c_8191,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,empty_set),sK21(X0,empty_set)),X0)
| ( relation_inverse(X0) = empty_set )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8124,c_135]) ).
tcf(c_8195,plain,
! [X0: $i] :
( in(ordered_pair(sK21(empty_set,X0),sK22(empty_set,X0)),X0)
| ( relation_inverse(empty_set) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8123,c_135]) ).
tcf(c_8227,plain,
empty(relation_inverse(empty_set)),
inference(global_subsumption_just,[status(thm)],[c_4289,c_136,c_4301]) ).
tcf(c_8229,plain,
! [X0: $i] :
( ( relation_inverse(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8227,c_66]) ).
tcf(c_8232,plain,
relation_inverse(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_8227,c_133]) ).
tcf(c_8233,plain,
relation(relation_inverse(empty_set)),
inference(superposition,[status(thm)],[c_8227,c_94]) ).
tcf(c_8234,plain,
function(relation_inverse(empty_set)),
inference(superposition,[status(thm)],[c_8227,c_85]) ).
tcf(c_8252,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(X1,X0),empty_set)
| ~ relation(empty_set)
| ~ in(ordered_pair(X0,X1),empty_set) ),
inference(superposition,[status(thm)],[c_8232,c_297]) ).
tcf(c_8258,plain,
( function(relation_rng(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_4367]) ).
tcf(c_8273,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_77,c_4259]) ).
tcf(c_8276,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_rng(sK1) = X0 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_105,c_4259]) ).
tcf(c_8277,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_107,c_4259]) ).
tcf(c_8278,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_4259]) ).
tcf(c_8279,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_4259]) ).
tcf(c_8280,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_4259]) ).
tcf(c_8281,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_4259]) ).
tcf(c_8289,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5969,c_4259]) ).
tcf(c_8290,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5929,c_4259]) ).
tcf(c_8291,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5964,c_4259]) ).
tcf(c_8292,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_5914,c_4259]) ).
tcf(c_8293,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_8277,c_4013]) ).
tcf(c_8294,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8293,c_64]) ).
tcf(c_8297,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_8276,c_4013]) ).
tcf(c_8298,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8297,c_64]) ).
tcf(c_8302,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8273,c_64]) ).
tcf(c_8306,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8292,c_64]) ).
tcf(c_8310,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8290,c_64]) ).
tcf(c_8314,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8291,c_64]) ).
tcf(c_8318,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8289,c_64]) ).
tcf(c_8322,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8281,c_64]) ).
tcf(c_8327,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8280,c_64]) ).
tcf(c_8332,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8279,c_64]) ).
tcf(c_8337,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8278,c_64]) ).
tcf(c_8391,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK1),sK15(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8294,c_70]) ).
tcf(c_8392,plain,
! [X0: $i] :
( element(sK15(sK1,X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_69]) ).
tcf(c_8393,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_67]) ).
tcf(c_8394,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_5348]) ).
tcf(c_8395,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_4619]) ).
tcf(c_8396,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_4406]) ).
tcf(c_8421,plain,
! [X0: $i] :
( in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8298,c_70]) ).
tcf(c_8422,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_8298,c_69]) ).
tcf(c_8423,plain,
! [X0: $i] :
( in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_67]) ).
tcf(c_8424,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8298,c_5348]) ).
tcf(c_8425,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8298,c_4619]) ).
tcf(c_8426,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8298,c_4406]) ).
tcf(c_8427,plain,
( in(sK14(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_8298,c_8115]) ).
tcf(c_8429,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ in(relation_dom(sK1),sK14(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8298,c_70]) ).
tcf(c_8430,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_8298,c_69]) ).
tcf(c_8431,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8298,c_67]) ).
tcf(c_8433,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8298,c_4619]) ).
tcf(c_8434,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8298,c_4406]) ).
tcf(c_8495,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_7652]) ).
tcf(c_8519,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_8495]) ).
tcf(c_8539,plain,
! [X0: $i] :
( in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8302,c_70]) ).
tcf(c_8540,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_8302,c_69]) ).
tcf(c_8541,plain,
! [X0: $i] :
( in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_67]) ).
tcf(c_8545,plain,
( in(sK5(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK1) = empty_set ) ),
inference(superposition,[status(thm)],[c_8302,c_8115]) ).
tcf(c_8546,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8302,c_4468]) ).
tcf(c_8547,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ in(relation_dom(sK1),sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8302,c_70]) ).
tcf(c_8548,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| element(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_8302,c_69]) ).
tcf(c_8549,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8302,c_67]) ).
tcf(c_8551,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8302,c_4619]) ).
tcf(c_8552,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8302,c_4406]) ).
tcf(c_8600,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_6800,c_4039,c_8519]) ).
tcf(c_8612,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_8306,c_70]) ).
tcf(c_8613,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_8306,c_69]) ).
tcf(c_8614,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8306,c_67]) ).
tcf(c_8615,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8306,c_4468]) ).
tcf(c_8633,plain,
relation_dom(relation_inverse(sK1)) = relation_rng(sK1),
inference(superposition,[status(thm)],[c_64,c_71]) ).
tcf(c_8643,plain,
relation_dom(relation_inverse(relation_inverse(sK1))) = relation_rng(relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_7106,c_71]) ).
tcf(c_8646,plain,
relation_dom(relation_inverse(sK1)) = relation_dom(sK2),
inference(light_normalisation,[status(thm)],[c_8633,c_5364]) ).
tcf(c_8648,plain,
relation_rng(relation_inverse(sK1)) = relation_dom(sK1),
inference(light_normalisation,[status(thm)],[c_8643,c_7208]) ).
tcf(c_8668,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_8310,c_70]) ).
tcf(c_8669,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_8310,c_69]) ).
tcf(c_8670,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8310,c_67]) ).
tcf(c_8671,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8310,c_4468]) ).
tcf(c_8690,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(sK2)
| ~ empty(relation_inverse(sK1)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_8695,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_4031,c_8600]) ).
tcf(c_8704,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_87]) ).
tcf(c_8705,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_5332]) ).
tcf(c_8706,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8695,c_4791]) ).
tcf(c_8716,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8704,c_65,c_64]) ).
tcf(c_8736,plain,
( relation(relation_rng(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_4368]) ).
tcf(c_8743,plain,
( empty(relation_rng(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_4369]) ).
tcf(c_8750,plain,
( function(relation_rng(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_5408]) ).
tcf(c_8757,plain,
( relation(relation_rng(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_5409]) ).
tcf(c_8766,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_8314,c_70]) ).
tcf(c_8767,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8314,c_69]) ).
tcf(c_8768,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8314,c_67]) ).
tcf(c_8770,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8314,c_4619]) ).
tcf(c_8771,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8314,c_4406]) ).
tcf(c_8793,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK1),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_8318,c_70]) ).
tcf(c_8794,plain,
( element(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8318,c_69]) ).
tcf(c_8795,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8318,c_67]) ).
tcf(c_8797,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8318,c_4619]) ).
tcf(c_8798,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8318,c_4406]) ).
tcf(c_8856,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(sK1,X0),sK24(sK1,X0))) ),
inference(superposition,[status(thm)],[c_8322,c_70]) ).
tcf(c_8857,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| element(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8322,c_69]) ).
tcf(c_8858,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8322,c_67]) ).
tcf(c_8859,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| in(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8322,c_106]) ).
tcf(c_8860,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8322,c_78]) ).
tcf(c_8861,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ( apply(X0,sK23(sK1,X0)) = sK24(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8322,c_197]) ).
tcf(c_8862,plain,
! [X0: $i] :
( in(sK23(sK1,relation_inverse(X0)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(X0)),sK23(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_8322,c_297]) ).
tcf(c_8863,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(superposition,[status(thm)],[c_8322,c_129]) ).
tcf(c_8864,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_5348]) ).
tcf(c_8865,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_4619]) ).
tcf(c_8866,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_4406]) ).
tcf(c_8870,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_3719]) ).
tcf(c_8871,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_8322,c_8115]) ).
tcf(c_8872,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_4468]) ).
tcf(c_8873,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8871,c_135]) ).
tcf(c_8900,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8863,c_64]) ).
tcf(c_8910,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(sK1)),sK23(sK1,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8870,c_3611]) ).
tcf(c_8935,plain,
( empty(sK10)
| ~ relation(sK10)
| ~ empty(relation_dom(sK10)) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_8975,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK23(X0,sK1),sK24(X0,sK1))) ),
inference(superposition,[status(thm)],[c_8327,c_70]) ).
tcf(c_8976,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| element(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8327,c_69]) ).
tcf(c_8977,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8327,c_67]) ).
tcf(c_8978,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| in(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8327,c_106]) ).
tcf(c_8979,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8327,c_78]) ).
tcf(c_8980,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ( apply(X0,sK23(X0,sK1)) = sK24(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8327,c_197]) ).
tcf(c_8981,plain,
! [X0: $i] :
( in(sK23(relation_inverse(X0),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(X0),sK1),sK23(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_8327,c_297]) ).
tcf(c_8983,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_5348]) ).
tcf(c_8984,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_4619]) ).
tcf(c_8985,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_4406]) ).
tcf(c_8989,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_3719]) ).
tcf(c_8990,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_8327,c_8115]) ).
tcf(c_8991,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_4468]) ).
tcf(c_8992,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8990,c_135]) ).
tcf(c_9024,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(sK1),sK1),sK23(relation_inverse(sK1),sK1)),sK1)
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8989,c_3611]) ).
tcf(c_9065,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK22(X0,sK1),sK21(X0,sK1))) ),
inference(superposition,[status(thm)],[c_8332,c_70]) ).
tcf(c_9066,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| element(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8332,c_69]) ).
tcf(c_9067,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8332,c_67]) ).
tcf(c_9068,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| in(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8332,c_106]) ).
tcf(c_9069,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8332,c_78]) ).
tcf(c_9070,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ( apply(X0,sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8332,c_197]) ).
tcf(c_9071,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_8332,c_124]) ).
tcf(c_9072,plain,
! [X0: $i] :
( in(sK21(relation_inverse(X0),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(X0),sK1),sK22(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK1 )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_8332,c_297]) ).
tcf(c_9073,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_5348]) ).
tcf(c_9074,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_4619]) ).
tcf(c_9075,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_4406]) ).
tcf(c_9076,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_8332,c_4259]) ).
tcf(c_9080,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( relation_inverse(empty_set) = sK1 )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_8332,c_8115]) ).
tcf(c_9081,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_4468]) ).
tcf(c_9082,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ relation(empty_set) ),
inference(light_normalisation,[status(thm)],[c_9080,c_8232]) ).
tcf(c_9083,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9082,c_135]) ).
tcf(c_9090,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9076,c_64]) ).
tcf(c_9114,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9071,c_64]) ).
tcf(c_9184,plain,
( empty(sK10)
| ~ relation(sK10)
| ~ empty(relation_rng(sK10)) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_9198,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_9090,c_70]) ).
tcf(c_9199,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_9090,c_69]) ).
tcf(c_9200,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9090,c_67]) ).
tcf(c_9202,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_9090,c_4619]) ).
tcf(c_9203,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_9090,c_4406]) ).
tcf(c_9227,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(X0,ordered_pair(sK21(sK1,X0),sK22(sK1,X0))) ),
inference(superposition,[status(thm)],[c_8337,c_70]) ).
tcf(c_9228,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| element(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8337,c_69]) ).
tcf(c_9229,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8337,c_67]) ).
tcf(c_9230,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8337,c_106]) ).
tcf(c_9231,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8337,c_78]) ).
tcf(c_9232,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ( apply(X0,sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8337,c_197]) ).
tcf(c_9233,plain,
! [X0: $i] :
( in(sK22(sK1,relation_inverse(X0)),relation_dom(sK1))
| in(ordered_pair(sK22(sK1,relation_inverse(X0)),sK21(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ~ relation(X0)
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_8337,c_297]) ).
tcf(c_9234,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_5348]) ).
tcf(c_9235,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_4619]) ).
tcf(c_9236,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_4406]) ).
tcf(c_9241,plain,
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ relation(empty_set) ),
inference(superposition,[status(thm)],[c_8337,c_8115]) ).
tcf(c_9242,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_4468]) ).
tcf(c_9243,plain,
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ( relation_inverse(sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9241,c_135]) ).
tcf(c_9333,plain,
( empty(relation_rng(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_5410]) ).
tcf(c_9340,plain,
( empty(relation_inverse(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_101,c_5417]) ).
tcf(c_9347,plain,
( function(relation_dom(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_6976]) ).
tcf(c_9354,plain,
( relation(relation_dom(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_6977]) ).
tcf(c_9363,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_8716,c_70]) ).
tcf(c_9364,plain,
( element(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8716,c_69]) ).
tcf(c_9365,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8716,c_67]) ).
tcf(c_9366,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8716,c_106]) ).
tcf(c_9371,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8716,c_3784]) ).
tcf(c_9375,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_9366,c_4013]) ).
tcf(c_9390,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_89,c_8393]) ).
tcf(c_9391,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_8393]) ).
tcf(c_9392,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_8393]) ).
tcf(c_9393,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_87,c_8393]) ).
tcf(c_9394,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_8393]) ).
tcf(c_9395,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_8393]) ).
tcf(c_9396,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8393]) ).
tcf(c_9397,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8393]) ).
tcf(c_9398,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8393]) ).
tcf(c_9399,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8393]) ).
tcf(c_9401,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_8393]) ).
tcf(c_9403,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5275,c_8393]) ).
tcf(c_9404,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8302,c_8393]) ).
tcf(c_9405,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5335,c_8393]) ).
tcf(c_9406,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5141,c_8393]) ).
tcf(c_9412,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_8393]) ).
tcf(c_9413,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_8393]) ).
tcf(c_9414,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_8393]) ).
tcf(c_9415,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_8393]) ).
tcf(c_9416,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_8393]) ).
tcf(c_9417,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_8393]) ).
tcf(c_9418,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_8393]) ).
tcf(c_9419,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_8393]) ).
tcf(c_9420,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_8393]) ).
tcf(c_9421,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_8393]) ).
tcf(c_9422,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_8393]) ).
tcf(c_9423,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_8393]) ).
tcf(c_9426,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8306,c_8393]) ).
tcf(c_9428,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6686,c_8393]) ).
tcf(c_9443,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9390,c_62,c_61]) ).
tcf(c_9606,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_73,c_9443]) ).
tcf(c_9607,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_9443]) ).
tcf(c_9636,plain,
( empty(relation_dom(sK12))
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_6978]) ).
tcf(c_9648,plain,
( relation(relation_dom(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_7009]) ).
tcf(c_9655,plain,
( function(relation_dom(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_7008]) ).
tcf(c_9662,plain,
( empty(relation_dom(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_7010]) ).
tcf(c_9671,plain,
( empty(relation_inverse(sK2))
| ~ relation(sK2)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_123,c_3994]) ).
tcf(c_9676,plain,
( empty(relation_inverse(sK2))
| ~ empty(relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9671,c_61]) ).
tcf(c_9685,plain,
( empty(relation_inverse(sK2))
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_101,c_9676]) ).
tcf(c_9688,plain,
( empty(relation_inverse(sK2))
| ~ empty(relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_4105,c_4128,c_4698,c_9685]) ).
tcf(c_9695,plain,
( empty(relation_inverse(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_9688]) ).
tcf(c_9702,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_4546,c_70]) ).
tcf(c_9703,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_69]) ).
tcf(c_9704,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_67]) ).
tcf(c_9705,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK5(relation_dom(sK2),X0),X1)) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(sK5(relation_dom(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_4546,c_76]) ).
tcf(c_9706,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK2)))
| ( apply(relation_inverse(sK1),ordered_pair(X0,X1)) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_106]) ).
tcf(c_9707,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK2)))
| ( apply(relation_inverse(sK1),ordered_pair(X0,X1)) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_78]) ).
tcf(c_9708,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK2),X0) = X1 )
| ( apply(relation_inverse(sK1),ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_197]) ).
tcf(c_9709,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(X1,sK13(relation_dom(sK2),X0))) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(sK13(relation_dom(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_4546,c_104]) ).
tcf(c_9710,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0) ),
inference(superposition,[status(thm)],[c_4546,c_124]) ).
tcf(c_9711,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_4546,c_129]) ).
tcf(c_9712,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4546,c_8393]) ).
tcf(c_9713,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_4546,c_4468]) ).
tcf(c_9794,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_6247]) ).
tcf(c_9800,plain,
( ( relation_dom(sK1) = empty_set )
| ~ in(relation_dom(sK2),sK6(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8128,c_70]) ).
tcf(c_9801,plain,
( element(sK6(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK1) = empty_set ) ),
inference(superposition,[status(thm)],[c_8128,c_69]) ).
tcf(c_9802,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8128,c_67]) ).
tcf(c_9803,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8128,c_8393]) ).
tcf(c_9804,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8128,c_4468]) ).
tcf(c_9829,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3333]) ).
tcf(c_9830,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3333]) ).
tcf(c_9831,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3333]) ).
tcf(c_9833,plain,
( ( relation_inverse(relation_inverse(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3333]) ).
tcf(c_9834,plain,
( ( relation_inverse(relation_dom(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3333]) ).
tcf(c_9835,plain,
( ( relation_inverse(relation_dom(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3333]) ).
tcf(c_9840,plain,
( ( sK1 = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_9833,c_3625]) ).
tcf(c_9852,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8646,c_75]) ).
tcf(c_9854,plain,
( relation(relation_dom(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8646,c_74]) ).
tcf(c_9855,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8646,c_73]) ).
tcf(c_9862,plain,
( empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9852,c_7106]) ).
tcf(c_9877,plain,
( ( relation_inverse(relation_inverse(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3333]) ).
tcf(c_9878,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9695,c_66]) ).
tcf(c_9879,plain,
( ( relation_rng(relation_inverse(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3330]) ).
tcf(c_9880,plain,
( ( relation_dom(relation_inverse(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3327]) ).
tcf(c_9881,plain,
( ( relation_inverse(sK2) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_133]) ).
tcf(c_9882,plain,
( relation(relation_inverse(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_94]) ).
tcf(c_9883,plain,
( function(relation_inverse(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_85]) ).
tcf(c_9887,plain,
( empty(relation_rng(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3997]) ).
tcf(c_9888,plain,
( relation(relation_rng(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3996]) ).
tcf(c_9889,plain,
( function(relation_rng(sK2))
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3995]) ).
tcf(c_9903,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(sK1) ),
inference(light_normalisation,[status(thm)],[c_9880,c_3805]) ).
tcf(c_9907,plain,
( ( sK2 = empty_set )
| ~ empty(sK1) ),
inference(light_normalisation,[status(thm)],[c_9877,c_3624]) ).
tcf(c_9913,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_9878]) ).
tcf(c_9926,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK2))) = relation_dom(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9882,c_72]) ).
tcf(c_9927,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK2))) = relation_rng(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9882,c_71]) ).
tcf(c_9928,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK2))) = relation_inverse(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9882,c_120]) ).
tcf(c_9948,plain,
( ( relation_inverse(relation_rng(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3333]) ).
tcf(c_9949,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9887,c_66]) ).
tcf(c_9950,plain,
( ( relation_rng(relation_rng(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3330]) ).
tcf(c_9951,plain,
( ( relation_dom(relation_rng(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3327]) ).
tcf(c_9966,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(sK1) ),
inference(instantiation,[status(thm)],[c_9949]) ).
tcf(c_9983,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK2),sK13(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8131,c_70]) ).
tcf(c_9984,plain,
( element(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_8131,c_69]) ).
tcf(c_9985,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8131,c_67]) ).
tcf(c_9986,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8131,c_8393]) ).
tcf(c_9987,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = sK15(sK1,sK13(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8131,c_4468]) ).
tcf(c_10000,plain,
( relation(relation_dom(sK1))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8648,c_102]) ).
tcf(c_10028,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK1),sK14(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8427,c_70]) ).
tcf(c_10029,plain,
( element(sK14(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set ) ),
inference(superposition,[status(thm)],[c_8427,c_69]) ).
tcf(c_10032,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8427,c_4619]) ).
tcf(c_10033,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8427,c_4406]) ).
tcf(c_10046,plain,
( ( relation_dom(sK1) = empty_set )
| ~ in(relation_dom(sK1),sK5(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8545,c_70]) ).
tcf(c_10047,plain,
( element(sK5(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK1) = empty_set ) ),
inference(superposition,[status(thm)],[c_8545,c_69]) ).
tcf(c_10050,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8545,c_4619]) ).
tcf(c_10051,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8545,c_4406]) ).
tcf(c_10072,plain,
~ empty(relation_rng(sK10)),
inference(global_subsumption_just,[status(thm)],[c_4929,c_91,c_90,c_9184]) ).
tcf(c_10079,plain,
~ empty(relation_dom(sK10)),
inference(global_subsumption_just,[status(thm)],[c_7033,c_91,c_90,c_8935]) ).
tcf(c_10087,plain,
( ( relation_rng(relation_inverse(relation_rng(sK2))) = relation_dom(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9888,c_72]) ).
tcf(c_10088,plain,
( ( relation_dom(relation_inverse(relation_rng(sK2))) = relation_rng(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9888,c_71]) ).
tcf(c_10089,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK2))) = relation_rng(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9888,c_120]) ).
tcf(c_10110,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(relation_dom(sK2),sK20(relation_dom(sK2)))
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_6246]) ).
tcf(c_10122,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_4410,c_70]) ).
tcf(c_10123,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_69]) ).
tcf(c_10124,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_67]) ).
tcf(c_10125,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_106]) ).
tcf(c_10126,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_78]) ).
tcf(c_10127,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_197]) ).
tcf(c_10128,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_104]) ).
tcf(c_10129,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_4259]) ).
tcf(c_10131,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4410,c_3784]) ).
tcf(c_10144,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10127,c_65,c_64]) ).
tcf(c_10147,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_10128,c_4013]) ).
tcf(c_10148,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10147,c_64]) ).
tcf(c_10190,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_10144]) ).
tcf(c_10191,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)))) = ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_10144]) ).
tcf(c_10192,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(X0,sK7(relation_dom(sK2),X0)))) = ordered_pair(X0,sK7(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_10144]) ).
tcf(c_10193,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(X0,apply(relation_dom(sK2),X0)))) = 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_87,c_10144]) ).
tcf(c_10194,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)))) = ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_10144]) ).
tcf(c_10195,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK15(relation_dom(sK2),X0),X0))) = ordered_pair(sK15(relation_dom(sK2),X0),X0) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_10144]) ).
tcf(c_10196,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) = ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_10144]) ).
tcf(c_10197,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))))) = ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_10144]) ).
tcf(c_10198,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) = ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_10144]) ).
tcf(c_10199,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)))) = ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_10144]) ).
tcf(c_10200,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_3448,c_10144]) ).
tcf(c_10201,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_4546,c_10144]) ).
tcf(c_10202,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_10144]) ).
tcf(c_10203,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_10144]) ).
tcf(c_10204,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5275,c_10144]) ).
tcf(c_10205,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8302,c_10144]) ).
tcf(c_10206,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5335,c_10144]) ).
tcf(c_10207,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5141,c_10144]) ).
tcf(c_10208,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5335,c_10144]) ).
tcf(c_10212,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5542,c_10144]) ).
tcf(c_10213,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_10144]) ).
tcf(c_10214,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_10144]) ).
tcf(c_10215,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_10144]) ).
tcf(c_10216,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_10144]) ).
tcf(c_10217,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_10144]) ).
tcf(c_10218,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_10144]) ).
tcf(c_10219,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_10144]) ).
tcf(c_10220,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_10144]) ).
tcf(c_10221,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_10144]) ).
tcf(c_10222,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_10144]) ).
tcf(c_10223,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_10144]) ).
tcf(c_10224,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_10144]) ).
tcf(c_10225,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8310,c_10144]) ).
tcf(c_10226,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7149,c_10144]) ).
tcf(c_10227,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8306,c_10144]) ).
tcf(c_10228,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6706,c_10144]) ).
tcf(c_10229,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6686,c_10144]) ).
tcf(c_10230,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8128,c_10144]) ).
tcf(c_10231,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8131,c_10144]) ).
tcf(c_10244,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10190,c_62,c_61]) ).
tcf(c_10490,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_87]) ).
tcf(c_10491,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(relation_dom(sK2),X0)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_6246]) ).
tcf(c_10492,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_6247]) ).
tcf(c_10493,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_5332]) ).
tcf(c_10494,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10244,c_4791]) ).
tcf(c_10510,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10490,c_65,c_64]) ).
tcf(c_10568,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_89,c_10148]) ).
tcf(c_10569,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_4546,c_10148]) ).
tcf(c_10574,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_8131,c_10148]) ).
tcf(c_10578,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10568,c_62,c_61]) ).
tcf(c_10590,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_dom(X0))) = empty_set )
| ( apply(X0,sK13(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_10578]) ).
tcf(c_10592,plain,
! [X0: $i] :
( in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8298,c_10578]) ).
tcf(c_10593,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5563,c_10578]) ).
tcf(c_10594,plain,
! [X0: $i] :
( in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5542,c_10578]) ).
tcf(c_10641,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_10510,c_70]) ).
tcf(c_10642,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10510,c_69]) ).
tcf(c_10644,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10510,c_106]) ).
tcf(c_10647,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10510,c_104]) ).
tcf(c_10650,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10510,c_3784]) ).
tcf(c_10651,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_10644,c_4013]) ).
tcf(c_10662,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_10647,c_4013]) ).
tcf(c_10673,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_4840,c_107]) ).
tcf(c_10674,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4840,c_8391]) ).
tcf(c_10675,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4840,c_8392]) ).
tcf(c_10676,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4840,c_8294]) ).
tcf(c_10689,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_10673,c_4013]) ).
tcf(c_10690,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10689,c_64]) ).
tcf(c_10715,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_10124]) ).
tcf(c_10716,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_10124]) ).
tcf(c_10717,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_87,c_10124]) ).
tcf(c_10718,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_10124]) ).
tcf(c_10719,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_10124]) ).
tcf(c_10720,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_10124]) ).
tcf(c_10721,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_10124]) ).
tcf(c_10722,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_10124]) ).
tcf(c_10723,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_10124]) ).
tcf(c_10725,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4546,c_10124]) ).
tcf(c_10726,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_10124]) ).
tcf(c_10728,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5275,c_10124]) ).
tcf(c_10729,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_8302,c_10124]) ).
tcf(c_10730,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5335,c_10124]) ).
tcf(c_10731,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5141,c_10124]) ).
tcf(c_10732,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5335,c_10124]) ).
tcf(c_10736,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5542,c_10124]) ).
tcf(c_10737,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_10124]) ).
tcf(c_10738,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_10124]) ).
tcf(c_10739,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_10124]) ).
tcf(c_10740,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_10124]) ).
tcf(c_10741,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_10124]) ).
tcf(c_10742,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_10124]) ).
tcf(c_10743,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_10124]) ).
tcf(c_10744,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_10124]) ).
tcf(c_10745,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_10124]) ).
tcf(c_10746,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_10124]) ).
tcf(c_10747,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_10124]) ).
tcf(c_10748,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_10124]) ).
tcf(c_10749,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_8310,c_10124]) ).
tcf(c_10750,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_7149,c_10124]) ).
tcf(c_10751,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_8306,c_10124]) ).
tcf(c_10752,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_6706,c_10124]) ).
tcf(c_10753,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_6686,c_10124]) ).
tcf(c_10754,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_8128,c_10124]) ).
tcf(c_11024,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(X0)) = relation_inverse(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_957]) ).
tcf(c_11025,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(X0)) = relation_inverse(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_957]) ).
tcf(c_11026,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(X0)) = relation_inverse(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_957]) ).
tcf(c_11027,plain,
function_inverse(empty_set) = relation_inverse(empty_set),
inference(superposition,[status(thm)],[c_136,c_957]) ).
tcf(c_11028,plain,
( ( function_inverse(relation_inverse(sK1)) = relation_inverse(relation_inverse(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_957]) ).
tcf(c_11029,plain,
( ( function_inverse(relation_dom(sK1)) = relation_inverse(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_957]) ).
tcf(c_11030,plain,
( ( function_inverse(relation_inverse(sK2)) = relation_inverse(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_957]) ).
tcf(c_11031,plain,
( ( function_inverse(relation_rng(sK2)) = relation_inverse(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_957]) ).
tcf(c_11032,plain,
( ( function_inverse(relation_dom(sK2)) = relation_inverse(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_957]) ).
tcf(c_11033,plain,
function_inverse(empty_set) = empty_set,
inference(light_normalisation,[status(thm)],[c_11027,c_8232]) ).
tcf(c_11038,plain,
( ( function_inverse(relation_inverse(sK2)) = sK2 )
| ~ empty(sK1) ),
inference(light_normalisation,[status(thm)],[c_11030,c_3624]) ).
tcf(c_11043,plain,
( ( function_inverse(relation_inverse(sK1)) = sK1 )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_11028,c_3625]) ).
tcf(c_11133,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_10726]) ).
tcf(c_11134,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_10726]) ).
tcf(c_11135,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_10726]) ).
tcf(c_11136,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_10726]) ).
tcf(c_11137,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_10726]) ).
tcf(c_11138,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10726]) ).
tcf(c_11139,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10726]) ).
tcf(c_11140,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10726]) ).
tcf(c_11141,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10726]) ).
tcf(c_11146,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_8298,c_10726]) ).
tcf(c_11147,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5563,c_10726]) ).
tcf(c_11148,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5542,c_10726]) ).
tcf(c_11149,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_10726]) ).
tcf(c_11150,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_10726]) ).
tcf(c_11151,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_10726]) ).
tcf(c_11152,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_10726]) ).
tcf(c_11153,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_10726]) ).
tcf(c_11154,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_10726]) ).
tcf(c_11155,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_10726]) ).
tcf(c_11156,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_10726]) ).
tcf(c_11157,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_10726]) ).
tcf(c_11158,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_10726]) ).
tcf(c_11159,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_10726]) ).
tcf(c_11160,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_10726]) ).
tcf(c_11295,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3401]) ).
tcf(c_11296,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3401]) ).
tcf(c_11297,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3401]) ).
tcf(c_11298,plain,
relation_dom(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3401]) ).
tcf(c_11299,plain,
( ( relation_dom(relation_dom(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3401]) ).
tcf(c_11300,plain,
( ( relation_dom(relation_dom(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3401]) ).
tcf(c_11301,plain,
( ( relation_dom(relation_dom(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3401]) ).
tcf(c_11302,plain,
( ( relation_dom(relation_dom(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3401]) ).
tcf(c_11303,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3401]) ).
tcf(c_11312,plain,
( ( relation_dom(relation_dom(sK2)) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_11299,c_4030]) ).
tcf(c_11341,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ in(sK1,ordered_pair(X0,sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_10690,c_70]) ).
tcf(c_11342,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_69]) ).
tcf(c_11343,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ empty(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_67]) ).
tcf(c_11344,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set )
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK7(sK1,sK5(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_76]) ).
tcf(c_11345,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_106]) ).
tcf(c_11346,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_78]) ).
tcf(c_11347,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_197]) ).
tcf(c_11350,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_3784]) ).
tcf(c_11369,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11347,c_65,c_64]) ).
tcf(c_11374,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set )
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK7(sK1,sK5(sK1,X0)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11344,c_64]) ).
tcf(c_11392,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_11369]) ).
tcf(c_11399,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(sK2,sK7(sK1,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11392,c_62,c_61]) ).
tcf(c_11416,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),empty_set),sK2)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11399,c_87]) ).
tcf(c_11421,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),empty_set),sK2)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11416,c_62,c_61]) ).
tcf(c_11461,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ in(sK2,ordered_pair(sK7(sK1,X0),empty_set)) ),
inference(superposition,[status(thm)],[c_11421,c_70]) ).
tcf(c_11462,plain,
! [X0: $i] :
( element(ordered_pair(sK7(sK1,X0),empty_set),sK2)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11421,c_69]) ).
tcf(c_11463,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ empty(sK2)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11421,c_67]) ).
tcf(c_11464,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ relation(sK2)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11421,c_106]) ).
tcf(c_11471,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11464,c_61]) ).
tcf(c_11564,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_11471]) ).
tcf(c_11565,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_11471]) ).
tcf(c_11586,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_89,c_11374]) ).
tcf(c_11589,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set )
| ~ in(sK5(sK1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11586,c_62,c_61]) ).
tcf(c_11607,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_dom(X0))) = empty_set )
| ( apply(X0,sK5(sK1,relation_dom(X0))) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,relation_dom(X0)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_11589]) ).
tcf(c_11608,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_11589]) ).
tcf(c_11609,plain,
! [X0: $i] :
( in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8302,c_11589]) ).
tcf(c_11610,plain,
! [X0: $i] :
( in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5335,c_11589]) ).
tcf(c_11611,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) )
| ( apply(sK2,sK7(sK1,sK5(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5141,c_11589]) ).
tcf(c_11658,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3402]) ).
tcf(c_11659,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3402]) ).
tcf(c_11660,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3402]) ).
tcf(c_11661,plain,
relation_dom(relation_rng(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3402]) ).
tcf(c_11662,plain,
( ( relation_dom(relation_rng(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3402]) ).
tcf(c_11663,plain,
( ( relation_dom(relation_rng(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3402]) ).
tcf(c_11664,plain,
( ( relation_dom(relation_rng(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3402]) ).
tcf(c_11665,plain,
( ( relation_dom(relation_rng(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3402]) ).
tcf(c_11666,plain,
( ( relation_dom(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3402]) ).
tcf(c_11689,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3403]) ).
tcf(c_11690,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3403]) ).
tcf(c_11691,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3403]) ).
tcf(c_11693,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3403]) ).
tcf(c_11694,plain,
( ( relation_dom(relation_inverse(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3403]) ).
tcf(c_11695,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3403]) ).
tcf(c_11696,plain,
( ( relation_dom(relation_inverse(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3403]) ).
tcf(c_11697,plain,
( ( relation_dom(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3403]) ).
tcf(c_11727,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3421]) ).
tcf(c_11728,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3421]) ).
tcf(c_11729,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3421]) ).
tcf(c_11730,plain,
relation_rng(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3421]) ).
tcf(c_11731,plain,
( ( relation_rng(relation_dom(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3421]) ).
tcf(c_11732,plain,
( ( relation_rng(relation_dom(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3421]) ).
tcf(c_11733,plain,
( ( relation_rng(relation_dom(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3421]) ).
tcf(c_11734,plain,
( ( relation_rng(relation_dom(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3421]) ).
tcf(c_11735,plain,
( ( relation_rng(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3421]) ).
tcf(c_11744,plain,
( ( relation_rng(relation_dom(sK2)) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_11731,c_4030]) ).
tcf(c_11769,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3422]) ).
tcf(c_11770,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3422]) ).
tcf(c_11771,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3422]) ).
tcf(c_11772,plain,
relation_rng(relation_rng(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_3422]) ).
tcf(c_11773,plain,
( ( relation_rng(relation_rng(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3422]) ).
tcf(c_11774,plain,
( ( relation_rng(relation_rng(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3422]) ).
tcf(c_11775,plain,
( ( relation_rng(relation_rng(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3422]) ).
tcf(c_11776,plain,
( ( relation_rng(relation_rng(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3422]) ).
tcf(c_11777,plain,
( ( relation_rng(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3422]) ).
tcf(c_11809,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3423]) ).
tcf(c_11810,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3423]) ).
tcf(c_11811,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3423]) ).
tcf(c_11813,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3423]) ).
tcf(c_11814,plain,
( ( relation_rng(relation_inverse(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3423]) ).
tcf(c_11815,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3423]) ).
tcf(c_11816,plain,
( ( relation_rng(relation_inverse(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3423]) ).
tcf(c_11817,plain,
( ( relation_rng(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3423]) ).
tcf(c_11839,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(powerset(X0)),X1),X1)
| ( relation_dom(sK20(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_77,c_4201]) ).
tcf(c_11840,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_dom(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_79,c_4201]) ).
tcf(c_11841,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(sK20(powerset(X1)))
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_dom(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_87,c_4201]) ).
tcf(c_11842,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(powerset(X0)),X1),X1)
| ( relation_rng(sK20(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_105,c_4201]) ).
tcf(c_11843,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_rng(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_107,c_4201]) ).
tcf(c_11844,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(sK20(powerset(X0)),X1),sK22(sK20(powerset(X0)),X1)),X1)
| ( relation_inverse(sK20(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_125,c_4201]) ).
tcf(c_11845,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,sK20(powerset(X0))),sK21(X1,sK20(powerset(X0)))),X1)
| ( sK20(powerset(X0)) = relation_inverse(X1) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_125,c_4201]) ).
tcf(c_11846,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,sK20(powerset(X0))),sK24(X1,sK20(powerset(X0)))),X1)
| ( sK20(powerset(X0)) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_130,c_4201]) ).
tcf(c_11847,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(sK20(powerset(X0)),X1),sK24(sK20(powerset(X0)),X1)),X1)
| ( sK20(powerset(X0)) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_130,c_4201]) ).
tcf(c_11848,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_3448,c_4201]) ).
tcf(c_11849,plain,
! [X0: $i] :
( in(sK5(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_4201]) ).
tcf(c_11850,plain,
! [X0: $i] :
( in(sK6(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_4201]) ).
tcf(c_11851,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(X0)))) = sK5(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_4201]) ).
tcf(c_11852,plain,
! [X0: $i] :
( in(sK14(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_4201]) ).
tcf(c_11853,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(X0)))) = sK14(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_4201]) ).
tcf(c_11854,plain,
! [X0: $i] :
( in(sK13(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_4201]) ).
tcf(c_11855,plain,
! [X0: $i] :
( in(sK23(sK20(powerset(X0)),sK1),relation_dom(sK1))
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8327,c_4201]) ).
tcf(c_11856,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(powerset(X0)),sK1)) = sK23(sK20(powerset(X0)),sK1) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5709,c_4201]) ).
tcf(c_11857,plain,
! [X0: $i] :
( in(sK24(sK20(powerset(X0)),sK1),relation_dom(sK2))
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5669,c_4201]) ).
tcf(c_11858,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8322,c_4201]) ).
tcf(c_11859,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(powerset(X0)))) = sK23(sK1,sK20(powerset(X0))) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5704,c_4201]) ).
tcf(c_11860,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5654,c_4201]) ).
tcf(c_11861,plain,
! [X0: $i] :
( in(sK21(sK20(powerset(X0)),sK1),relation_dom(sK1))
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8332,c_4201]) ).
tcf(c_11862,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(powerset(X0)),sK1)) = sK21(sK20(powerset(X0)),sK1) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5969,c_4201]) ).
tcf(c_11863,plain,
! [X0: $i] :
( in(sK22(sK20(powerset(X0)),sK1),relation_dom(sK2))
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5929,c_4201]) ).
tcf(c_11864,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8337,c_4201]) ).
tcf(c_11865,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(powerset(X0)))) = sK22(sK1,sK20(powerset(X0))) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5964,c_4201]) ).
tcf(c_11866,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5914,c_4201]) ).
tcf(c_12041,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_89,c_6132]) ).
tcf(c_12065,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12041,c_62,c_61]) ).
tcf(c_12139,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3423]) ).
tcf(c_12140,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3422]) ).
tcf(c_12141,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3421]) ).
tcf(c_12142,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3403]) ).
tcf(c_12143,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3402]) ).
tcf(c_12144,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3401]) ).
tcf(c_12145,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(X0))) = relation_inverse(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_957]) ).
tcf(c_12146,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3333]) ).
tcf(c_12147,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_66]) ).
tcf(c_12148,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3330]) ).
tcf(c_12149,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3327]) ).
tcf(c_12150,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_133]) ).
tcf(c_12151,plain,
! [X0: $i] :
( relation(sK20(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_94]) ).
tcf(c_12152,plain,
! [X0: $i] :
( function(sK20(powerset(X0)))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_85]) ).
tcf(c_12244,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(X0)))) = relation_dom(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_72]) ).
tcf(c_12245,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(X0)))) = relation_rng(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_71]) ).
tcf(c_12246,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(X0)))) = sK20(powerset(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_120]) ).
tcf(c_12264,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK1))
| ~ in(sK1,ordered_pair(X0,sK15(relation_inverse(sK1),X0))) ),
inference(superposition,[status(thm)],[c_4472,c_70]) ).
tcf(c_12265,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK15(relation_inverse(sK1),X0)),sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_69]) ).
tcf(c_12267,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_76]) ).
tcf(c_12268,plain,
! [X0: $i] :
( in(sK15(relation_inverse(sK1),X0),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_106]) ).
tcf(c_12270,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),X0) = apply(sK1,X0) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_197]) ).
tcf(c_12272,plain,
! [X0: $i] :
( in(sK15(relation_inverse(sK1),X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_4237]) ).
tcf(c_12273,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK15(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_3784]) ).
tcf(c_12282,plain,
! [X0: $i] :
( in(sK15(relation_inverse(sK1),X0),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_12268,c_4013]) ).
tcf(c_12284,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),X0) = apply(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12270,c_65,c_64]) ).
tcf(c_12287,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12267,c_64]) ).
tcf(c_12301,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(relation_inverse(sK1),X0) = apply(sK1,X0) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_12284]) ).
tcf(c_12302,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_12284]) ).
tcf(c_12303,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),ordered_pair(X0,sK7(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_12284]) ).
tcf(c_12304,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),ordered_pair(X0,apply(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_12284]) ).
tcf(c_12305,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_12284]) ).
tcf(c_12306,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),ordered_pair(sK15(relation_dom(sK1),X0),X0)) = apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_12284]) ).
tcf(c_12307,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12284]) ).
tcf(c_12308,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12284]) ).
tcf(c_12309,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12284]) ).
tcf(c_12310,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12284]) ).
tcf(c_12311,plain,
( empty(relation_dom(sK1))
| ( sK15(relation_inverse(sK1),sK20(relation_dom(sK1))) = apply(sK1,sK20(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_3448,c_12284]) ).
tcf(c_12315,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8298,c_12284]) ).
tcf(c_12316,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5563,c_12284]) ).
tcf(c_12317,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5542,c_12284]) ).
tcf(c_12318,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_12284]) ).
tcf(c_12319,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_12284]) ).
tcf(c_12320,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_12284]) ).
tcf(c_12321,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_12284]) ).
tcf(c_12322,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_12284]) ).
tcf(c_12323,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_12284]) ).
tcf(c_12324,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_12284]) ).
tcf(c_12325,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_12284]) ).
tcf(c_12326,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_12284]) ).
tcf(c_12327,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_12284]) ).
tcf(c_12328,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_12284]) ).
tcf(c_12329,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_12284]) ).
tcf(c_12330,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8318,c_12284]) ).
tcf(c_12331,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9090,c_12284]) ).
tcf(c_12332,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8314,c_12284]) ).
tcf(c_12333,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK5(sK1,X0)) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8302,c_12284]) ).
tcf(c_12334,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK14(sK1,X0)) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8298,c_12284]) ).
tcf(c_12335,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,X0)) = apply(sK1,sK15(sK1,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_12284]) ).
tcf(c_12336,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK14(sK1,empty_set)) = apply(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8427,c_12284]) ).
tcf(c_12337,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(relation_inverse(sK1),sK5(sK1,empty_set)) = apply(sK1,sK5(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8545,c_12284]) ).
tcf(c_12346,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(relation_inverse(sK1),X0) = apply(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12301,c_65,c_64]) ).
tcf(c_12598,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12346,c_107]) ).
tcf(c_12599,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12346,c_4472]) ).
tcf(c_12603,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_12598,c_3821]) ).
tcf(c_12604,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12603,c_3611]) ).
tcf(c_12616,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_89,c_12287]) ).
tcf(c_12621,plain,
( ( relation_dom(sK1) = empty_set )
| ~ in(sK5(sK1,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_8545,c_12287]) ).
tcf(c_12622,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK5(sK1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12616,c_65,c_64]) ).
tcf(c_12633,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_dom(X0))) = empty_set )
| ( apply(X0,sK5(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_12622]) ).
tcf(c_12634,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_12622]) ).
tcf(c_12635,plain,
! [X0: $i] :
( in(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8302,c_12622]) ).
tcf(c_12636,plain,
! [X0: $i] :
( in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5335,c_12622]) ).
tcf(c_12637,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5141,c_12622]) ).
tcf(c_12677,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4726,c_4623]) ).
tcf(c_12678,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4763,c_4623]) ).
tcf(c_12679,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4791,c_4623]) ).
tcf(c_12680,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7472,c_4623]) ).
tcf(c_12681,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_4623,c_70]) ).
tcf(c_12682,plain,
! [X0: $i] :
( element(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4623,c_69]) ).
tcf(c_12685,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4623,c_78]) ).
tcf(c_12686,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4623,c_197]) ).
tcf(c_12688,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4623,c_4259]) ).
tcf(c_12701,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12686,c_65,c_64]) ).
tcf(c_12753,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_12701]) ).
tcf(c_12754,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)))) = ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_12701]) ).
tcf(c_12755,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(X0,sK7(relation_dom(sK2),X0)))) = ordered_pair(X0,sK7(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_12701]) ).
tcf(c_12756,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(X0,apply(relation_dom(sK2),X0)))) = 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_87,c_12701]) ).
tcf(c_12757,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)))) = ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_12701]) ).
tcf(c_12758,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK15(relation_dom(sK2),X0),X0))) = ordered_pair(sK15(relation_dom(sK2),X0),X0) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_12701]) ).
tcf(c_12759,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) = ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_12701]) ).
tcf(c_12760,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))))) = ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_12701]) ).
tcf(c_12761,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) = ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_12701]) ).
tcf(c_12762,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)))) = ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_12701]) ).
tcf(c_12763,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_3448,c_12701]) ).
tcf(c_12764,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_4546,c_12701]) ).
tcf(c_12765,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_12701]) ).
tcf(c_12766,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_12701]) ).
tcf(c_12767,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5275,c_12701]) ).
tcf(c_12768,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8302,c_12701]) ).
tcf(c_12769,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5335,c_12701]) ).
tcf(c_12770,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5141,c_12701]) ).
tcf(c_12771,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5335,c_12701]) ).
tcf(c_12775,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5542,c_12701]) ).
tcf(c_12776,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_12701]) ).
tcf(c_12777,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_12701]) ).
tcf(c_12778,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_12701]) ).
tcf(c_12779,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_12701]) ).
tcf(c_12780,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_12701]) ).
tcf(c_12781,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_12701]) ).
tcf(c_12782,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_12701]) ).
tcf(c_12783,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_12701]) ).
tcf(c_12784,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_12701]) ).
tcf(c_12785,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_12701]) ).
tcf(c_12786,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_12701]) ).
tcf(c_12787,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_12701]) ).
tcf(c_12788,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8310,c_12701]) ).
tcf(c_12789,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7149,c_12701]) ).
tcf(c_12790,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8306,c_12701]) ).
tcf(c_12791,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6706,c_12701]) ).
tcf(c_12792,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6686,c_12701]) ).
tcf(c_12793,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8128,c_12701]) ).
tcf(c_12794,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8131,c_12701]) ).
tcf(c_12807,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12753,c_62,c_61]) ).
tcf(c_13069,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8695,c_4863]) ).
tcf(c_13070,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10244,c_4863]) ).
tcf(c_13071,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_4863,c_107]) ).
tcf(c_13072,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4863,c_8391]) ).
tcf(c_13073,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4863,c_8392]) ).
tcf(c_13074,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4863,c_8294]) ).
tcf(c_13087,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_13071,c_4013]) ).
tcf(c_13088,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13087,c_64]) ).
tcf(c_13133,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(powerset(X0)),X1),X1)
| element(ordered_pair(sK5(sK20(powerset(X0)),X1),sK6(sK20(powerset(X0)),X1)),X0)
| ( relation_dom(sK20(powerset(X0))) = X1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_77,c_4216]) ).
tcf(c_13134,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK7(sK20(powerset(X1)),X0)),X1)
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_dom(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_79,c_4216]) ).
tcf(c_13135,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(sK20(powerset(X1)),X0)),X1)
| ~ function(sK20(powerset(X1)))
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_dom(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_87,c_4216]) ).
tcf(c_13136,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(powerset(X0)),X1),X1)
| element(ordered_pair(sK14(sK20(powerset(X0)),X1),sK13(sK20(powerset(X0)),X1)),X0)
| ( relation_rng(sK20(powerset(X0))) = X1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_105,c_4216]) ).
tcf(c_13137,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK15(sK20(powerset(X1)),X0),X0),X1)
| ~ relation(sK20(powerset(X1)))
| ~ in(X0,relation_rng(sK20(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_107,c_4216]) ).
tcf(c_13138,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK22(sK20(powerset(X0)),X1),sK21(sK20(powerset(X0)),X1)),X0)
| in(ordered_pair(sK21(sK20(powerset(X0)),X1),sK22(sK20(powerset(X0)),X1)),X1)
| ( relation_inverse(sK20(powerset(X0))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_125,c_4216]) ).
tcf(c_13139,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK21(X1,sK20(powerset(X0))),sK22(X1,sK20(powerset(X0)))),X0)
| in(ordered_pair(sK22(X1,sK20(powerset(X0))),sK21(X1,sK20(powerset(X0)))),X1)
| ( sK20(powerset(X0)) = relation_inverse(X1) )
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_125,c_4216]) ).
tcf(c_13140,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(X1,sK20(powerset(X0))),sK24(X1,sK20(powerset(X0)))),X0)
| in(ordered_pair(sK23(X1,sK20(powerset(X0))),sK24(X1,sK20(powerset(X0)))),X1)
| ( sK20(powerset(X0)) = X1 )
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_130,c_4216]) ).
tcf(c_13141,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(sK20(powerset(X0)),X1),sK24(sK20(powerset(X0)),X1)),X0)
| in(ordered_pair(sK23(sK20(powerset(X0)),X1),sK24(sK20(powerset(X0)),X1)),X1)
| ( sK20(powerset(X0)) = X1 )
| ~ relation(X1)
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_130,c_4216]) ).
tcf(c_13142,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| element(sK20(sK20(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_3448,c_4216]) ).
tcf(c_13143,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| in(sK5(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8302,c_4216]) ).
tcf(c_13144,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| in(sK6(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_5335,c_4216]) ).
tcf(c_13145,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(X0)))) = sK5(sK1,sK20(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_5141,c_4216]) ).
tcf(c_13146,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| in(sK14(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8298,c_4216]) ).
tcf(c_13147,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(X0)))) = sK14(sK1,sK20(powerset(X0))) ) ),
inference(superposition,[status(thm)],[c_5563,c_4216]) ).
tcf(c_13148,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| in(sK13(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_5542,c_4216]) ).
tcf(c_13149,plain,
! [X0: $i] :
( in(sK23(sK20(powerset(X0)),sK1),relation_dom(sK1))
| element(ordered_pair(sK23(sK20(powerset(X0)),sK1),sK24(sK20(powerset(X0)),sK1)),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8327,c_4216]) ).
tcf(c_13150,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK20(powerset(X0)),sK1),sK24(sK20(powerset(X0)),sK1)),X0)
| ( sK20(powerset(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(powerset(X0)),sK1)) = sK23(sK20(powerset(X0)),sK1) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5709,c_4216]) ).
tcf(c_13151,plain,
! [X0: $i] :
( in(sK24(sK20(powerset(X0)),sK1),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(powerset(X0)),sK1),sK24(sK20(powerset(X0)),sK1)),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5669,c_4216]) ).
tcf(c_13152,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(powerset(X0))),relation_dom(sK1))
| element(ordered_pair(sK23(sK1,sK20(powerset(X0))),sK24(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8322,c_4216]) ).
tcf(c_13153,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,sK20(powerset(X0))),sK24(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(powerset(X0)))) = sK23(sK1,sK20(powerset(X0))) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5704,c_4216]) ).
tcf(c_13154,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(powerset(X0))),relation_dom(sK2))
| element(ordered_pair(sK23(sK1,sK20(powerset(X0))),sK24(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5654,c_4216]) ).
tcf(c_13155,plain,
! [X0: $i] :
( in(sK21(sK20(powerset(X0)),sK1),relation_dom(sK1))
| element(ordered_pair(sK22(sK20(powerset(X0)),sK1),sK21(sK20(powerset(X0)),sK1)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8332,c_4216]) ).
tcf(c_13156,plain,
! [X0: $i] :
( element(ordered_pair(sK22(sK20(powerset(X0)),sK1),sK21(sK20(powerset(X0)),sK1)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(powerset(X0)),sK1)) = sK21(sK20(powerset(X0)),sK1) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5969,c_4216]) ).
tcf(c_13157,plain,
! [X0: $i] :
( in(sK22(sK20(powerset(X0)),sK1),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(powerset(X0)),sK1),sK21(sK20(powerset(X0)),sK1)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5929,c_4216]) ).
tcf(c_13158,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(powerset(X0))),relation_dom(sK1))
| element(ordered_pair(sK21(sK1,sK20(powerset(X0))),sK22(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_8337,c_4216]) ).
tcf(c_13159,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,sK20(powerset(X0))),sK22(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(powerset(X0)))) = sK22(sK1,sK20(powerset(X0))) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5964,c_4216]) ).
tcf(c_13160,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(powerset(X0))),relation_dom(sK2))
| element(ordered_pair(sK21(sK1,sK20(powerset(X0))),sK22(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_5914,c_4216]) ).
tcf(c_13357,plain,
! [X0: $i] : apply(empty_set,X0) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_4519,c_136,c_3966,c_4519]) ).
tcf(c_13363,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_13357,c_87]) ).
tcf(c_13366,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_13363,c_3404]) ).
tcf(c_13374,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK13(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_8154,c_70]) ).
tcf(c_13375,plain,
! [X0: $i] :
( element(sK13(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_8154,c_69]) ).
tcf(c_13377,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1))) = apply(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8154,c_12284]) ).
tcf(c_13380,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8154,c_4619]) ).
tcf(c_13381,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8154,c_4406]) ).
tcf(c_13383,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8154,c_12701]) ).
tcf(c_13385,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8154,c_10144]) ).
tcf(c_13387,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = sK15(sK1,sK13(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8154,c_4468]) ).
tcf(c_13388,plain,
! [X0: $i] :
( element(sK13(empty_set,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8154,c_4216]) ).
tcf(c_13464,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_4763,c_12807]) ).
tcf(c_13465,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_12807]) ).
tcf(c_13469,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_87]) ).
tcf(c_13471,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(relation_dom(sK2),X0)
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_6246]) ).
tcf(c_13472,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_6247]) ).
tcf(c_13473,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_5332]) ).
tcf(c_13488,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13469,c_65,c_64]) ).
tcf(c_13595,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4726,c_13488]) ).
tcf(c_13596,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_13488]) ).
tcf(c_13597,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4791,c_13488]) ).
tcf(c_13598,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7472,c_13488]) ).
tcf(c_13599,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_13488,c_70]) ).
tcf(c_13600,plain,
! [X0: $i] :
( element(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13488,c_69]) ).
tcf(c_13602,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13488,c_106]) ).
tcf(c_13605,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13488,c_104]) ).
tcf(c_13609,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_13602,c_4013]) ).
tcf(c_13628,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_13605,c_4013]) ).
tcf(c_13648,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(sK1)
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_10732,c_70]) ).
tcf(c_13649,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_69]) ).
tcf(c_13650,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10732,c_67]) ).
tcf(c_13657,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_12701]) ).
tcf(c_13658,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_10124]) ).
tcf(c_13659,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_10144]) ).
tcf(c_13661,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_4468]) ).
tcf(c_13662,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_4216]) ).
tcf(c_13663,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10732,c_4201]) ).
tcf(c_13664,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_12622]) ).
tcf(c_13702,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_10736,c_70]) ).
tcf(c_13703,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_69]) ).
tcf(c_13705,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_12284]) ).
tcf(c_13708,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_4619]) ).
tcf(c_13709,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_4406]) ).
tcf(c_13716,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_4216]) ).
tcf(c_13717,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10736,c_4201]) ).
tcf(c_13718,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_10578]) ).
tcf(c_13751,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK6(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6281,c_70]) ).
tcf(c_13752,plain,
! [X0: $i] :
( element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_69]) ).
tcf(c_13753,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6281,c_67]) ).
tcf(c_13754,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_12701]) ).
tcf(c_13756,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_10144]) ).
tcf(c_13757,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6281,c_8393]) ).
tcf(c_13758,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK15(sK1,sK6(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_4468]) ).
tcf(c_13787,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK2))
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6287,c_70]) ).
tcf(c_13788,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_69]) ).
tcf(c_13796,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_12701]) ).
tcf(c_13798,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_10144]) ).
tcf(c_13799,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6287,c_8393]) ).
tcf(c_13800,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_4468]) ).
tcf(c_13801,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_4216]) ).
tcf(c_13802,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_4201]) ).
tcf(c_13803,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_12622]) ).
tcf(c_13837,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_12065,c_64,c_160,c_4154,c_4698,c_8690]) ).
tcf(c_13843,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_73,c_13837]) ).
tcf(c_13866,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6331,c_70]) ).
tcf(c_13867,plain,
! [X0: $i] :
( element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_69]) ).
tcf(c_13868,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6331,c_67]) ).
tcf(c_13869,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_12701]) ).
tcf(c_13871,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_10144]) ).
tcf(c_13872,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6331,c_8393]) ).
tcf(c_13873,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK15(sK1,sK13(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_4468]) ).
tcf(c_13875,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_6331,c_10148]) ).
tcf(c_13931,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),sK5(sK1,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_5251,c_87]) ).
tcf(c_13932,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5251,c_13488]) ).
tcf(c_13933,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_12807]) ).
tcf(c_13934,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5251,c_4623]) ).
tcf(c_13935,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_4763]) ).
tcf(c_13952,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),sK5(sK1,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_13931,c_4030]) ).
tcf(c_13953,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),sK5(sK1,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13952,c_987,c_3611]) ).
tcf(c_14021,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ in(X0,sK5(empty_set,X0)) ),
inference(superposition,[status(thm)],[c_8158,c_70]) ).
tcf(c_14022,plain,
! [X0: $i] :
( element(sK5(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_8158,c_69]) ).
tcf(c_14024,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1))) = apply(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8158,c_12284]) ).
tcf(c_14027,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8158,c_4619]) ).
tcf(c_14028,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8158,c_4406]) ).
tcf(c_14030,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8158,c_12701]) ).
tcf(c_14032,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8158,c_10144]) ).
tcf(c_14034,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = sK15(sK1,sK5(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8158,c_4468]) ).
tcf(c_14035,plain,
! [X0: $i] :
( element(sK5(empty_set,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8158,c_4216]) ).
tcf(c_14068,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_9829]) ).
tcf(c_14069,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_9829]) ).
tcf(c_14070,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_9829]) ).
tcf(c_14071,plain,
relation_inverse(relation_dom(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_9829]) ).
tcf(c_14072,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_9829]) ).
tcf(c_14073,plain,
( ( relation_inverse(relation_dom(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_9829]) ).
tcf(c_14074,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_9829]) ).
tcf(c_14075,plain,
( ( relation_inverse(relation_dom(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_9829]) ).
tcf(c_14076,plain,
( ( relation_inverse(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_9829]) ).
tcf(c_14077,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_9829]) ).
tcf(c_14086,plain,
( ( relation_inverse(relation_dom(sK2)) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_14072,c_4030]) ).
tcf(c_14153,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_9830]) ).
tcf(c_14154,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_9830]) ).
tcf(c_14155,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_9830]) ).
tcf(c_14156,plain,
relation_inverse(relation_rng(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_9830]) ).
tcf(c_14157,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_9830]) ).
tcf(c_14158,plain,
( ( relation_inverse(relation_rng(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_9830]) ).
tcf(c_14159,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_9830]) ).
tcf(c_14160,plain,
( ( relation_inverse(relation_rng(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_9830]) ).
tcf(c_14161,plain,
( ( relation_inverse(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_9830]) ).
tcf(c_14162,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_9830]) ).
tcf(c_14233,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_9831]) ).
tcf(c_14234,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_9831]) ).
tcf(c_14235,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_9831]) ).
tcf(c_14237,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_9831]) ).
tcf(c_14238,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_9831]) ).
tcf(c_14239,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_9831]) ).
tcf(c_14240,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_9831]) ).
tcf(c_14241,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_9831]) ).
tcf(c_14242,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_9831]) ).
tcf(c_14316,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK2))
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6337,c_70]) ).
tcf(c_14317,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_69]) ).
tcf(c_14319,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_12284]) ).
tcf(c_14321,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_5348]) ).
tcf(c_14322,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_4619]) ).
tcf(c_14323,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_4406]) ).
tcf(c_14330,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_4216]) ).
tcf(c_14331,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_4201]) ).
tcf(c_14332,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_10578]) ).
tcf(c_14371,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK14(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8423,c_70]) ).
tcf(c_14372,plain,
! [X0: $i] :
( element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_69]) ).
tcf(c_14374,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK14(sK1,X0)) = apply(sK1,sK14(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_12284]) ).
tcf(c_14377,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_4619]) ).
tcf(c_14378,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK14(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_4406]) ).
tcf(c_14400,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK1))
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8431,c_70]) ).
tcf(c_14401,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_69]) ).
tcf(c_14403,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_12284]) ).
tcf(c_14406,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_4619]) ).
tcf(c_14407,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_4406]) ).
tcf(c_14414,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_4216]) ).
tcf(c_14415,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_4201]) ).
tcf(c_14416,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_10578]) ).
tcf(c_14549,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8541,c_70]) ).
tcf(c_14550,plain,
! [X0: $i] :
( element(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_69]) ).
tcf(c_14552,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK5(sK1,X0)) = apply(sK1,sK5(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_12284]) ).
tcf(c_14555,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_4619]) ).
tcf(c_14556,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK5(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_4406]) ).
tcf(c_14558,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_8541,c_12287]) ).
tcf(c_14583,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK1))
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8549,c_70]) ).
tcf(c_14584,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_69]) ).
tcf(c_14592,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_12701]) ).
tcf(c_14594,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_10144]) ).
tcf(c_14595,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_8393]) ).
tcf(c_14596,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_4468]) ).
tcf(c_14597,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_4216]) ).
tcf(c_14598,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_4201]) ).
tcf(c_14599,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_12622]) ).
tcf(c_14724,plain,
( ~ empty(sK1)
| ( relation_inverse(sK1) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_10749,c_3684]) ).
tcf(c_14725,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(sK1) ),
inference(renaming,[status(thm)],[c_14724]) ).
tcf(c_14730,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_5291,c_4128,c_4760,c_13843]) ).
tcf(c_14739,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_14730,c_87]) ).
tcf(c_14740,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14730,c_13488]) ).
tcf(c_14741,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_14730,c_12807]) ).
tcf(c_14742,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14730,c_4623]) ).
tcf(c_14752,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_14739,c_4030]) ).
tcf(c_14753,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14752,c_987,c_3611]) ).
tcf(c_14778,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12150]) ).
tcf(c_14779,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12150]) ).
tcf(c_14780,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12150]) ).
tcf(c_14781,plain,
sK20(powerset(empty_set)) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12150]) ).
tcf(c_14782,plain,
( ( sK20(powerset(relation_inverse(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_12150]) ).
tcf(c_14783,plain,
( ( sK20(powerset(relation_dom(sK1))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_12150]) ).
tcf(c_14784,plain,
( ( sK20(powerset(relation_inverse(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_12150]) ).
tcf(c_14785,plain,
( ( sK20(powerset(relation_rng(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_12150]) ).
tcf(c_14786,plain,
( ( sK20(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_12150]) ).
tcf(c_14787,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12150]) ).
tcf(c_14810,plain,
( empty(powerset(empty_set))
| ~ in(powerset(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_14781,c_3486]) ).
tcf(c_14811,plain,
( empty(powerset(empty_set))
| in(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_14781,c_3448]) ).
tcf(c_14812,plain,
element(empty_set,powerset(empty_set)),
inference(superposition,[status(thm)],[c_14781,c_119]) ).
tcf(c_14823,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = empty_set )
| ~ in(X0,sK13(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_13375,c_114]) ).
tcf(c_14824,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK13(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_13375,c_113]) ).
tcf(c_14859,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_87]) ).
tcf(c_14860,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(relation_dom(sK2),X0)
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_6246]) ).
tcf(c_14861,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_6247]) ).
tcf(c_14862,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_5332]) ).
tcf(c_14876,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14859,c_65,c_64]) ).
tcf(c_14902,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4840,c_14876]) ).
tcf(c_14903,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4863,c_14876]) ).
tcf(c_14904,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK15(sK1,X0),X0)) ),
inference(superposition,[status(thm)],[c_14876,c_70]) ).
tcf(c_14905,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14876,c_69]) ).
tcf(c_14907,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14876,c_106]) ).
tcf(c_14910,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK15(sK1,sK13(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14876,c_104]) ).
tcf(c_14914,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_14907,c_4013]) ).
tcf(c_14930,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK15(sK1,sK13(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_14910,c_4013]) ).
tcf(c_14936,plain,
( ~ empty(relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_6779,c_3684,c_4128]) ).
tcf(c_14937,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK2)) ),
inference(renaming,[status(thm)],[c_14936]) ).
tcf(c_14942,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_73,c_14937]) ).
tcf(c_14946,plain,
( ~ empty(relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_9200,c_64,c_160,c_3684]) ).
tcf(c_14947,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_dom(sK1)) ),
inference(renaming,[status(thm)],[c_14946]) ).
tcf(c_14964,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_6420,c_87]) ).
tcf(c_14965,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6420,c_13488]) ).
tcf(c_14966,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6420,c_4623]) ).
tcf(c_14967,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6420,c_4763]) ).
tcf(c_14980,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_14964,c_4030]) ).
tcf(c_14981,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14980,c_987,c_3611]) ).
tcf(c_15015,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = empty_set )
| ~ in(X0,sK5(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_14022,c_114]) ).
tcf(c_15016,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = empty_set )
| ~ empty(X1)
| ~ in(X0,sK5(empty_set,powerset(X1))) ),
inference(superposition,[status(thm)],[c_14022,c_113]) ).
tcf(c_15029,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_3774]) ).
tcf(c_15032,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_rng(sK1) = X0 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_3774]) ).
tcf(c_15033,plain,
! [X0: $i] :
( ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_107,c_3774]) ).
tcf(c_15034,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_3774]) ).
tcf(c_15035,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_3774]) ).
tcf(c_15036,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_3774]) ).
tcf(c_15037,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_3774]) ).
tcf(c_15038,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_inverse(sK1))
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10510,c_3774]) ).
tcf(c_15040,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4472,c_3774]) ).
tcf(c_15041,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8716,c_3774]) ).
tcf(c_15042,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_inverse(sK1))
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13488,c_3774]) ).
tcf(c_15043,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4623,c_3774]) ).
tcf(c_15050,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_3774]) ).
tcf(c_15051,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_3774]) ).
tcf(c_15052,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_3774]) ).
tcf(c_15053,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_3774]) ).
tcf(c_15054,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_3774]) ).
tcf(c_15055,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_3774]) ).
tcf(c_15056,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ empty(relation_inverse(sK1))
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10690,c_3774]) ).
tcf(c_15057,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_inverse(sK1))
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14876,c_3774]) ).
tcf(c_15062,plain,
! [X0: $i] :
( ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_15033,c_4013]) ).
tcf(c_15067,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_15032,c_4013]) ).
tcf(c_15068,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15067,c_64]) ).
tcf(c_15072,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15029,c_64]) ).
tcf(c_15076,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15055,c_64]) ).
tcf(c_15080,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15053,c_64]) ).
tcf(c_15084,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15052,c_64]) ).
tcf(c_15088,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15050,c_64]) ).
tcf(c_15101,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15054,c_64]) ).
tcf(c_15105,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15051,c_64]) ).
tcf(c_15109,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15037,c_64]) ).
tcf(c_15114,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15036,c_64]) ).
tcf(c_15119,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15035,c_64]) ).
tcf(c_15124,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15034,c_64]) ).
tcf(c_15167,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK5(sK19(X0),X1),X1)
| element(ordered_pair(sK5(sK19(X0),X1),sK6(sK19(X0),X1)),X0)
| ( relation_dom(sK19(X0)) = X1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_77,c_4215]) ).
tcf(c_15168,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(ordered_pair(X0,sK7(sK19(X1),X0)),X1)
| ~ relation(sK19(X1))
| ~ in(X0,relation_dom(sK19(X1))) ),
inference(superposition,[status(thm)],[c_79,c_4215]) ).
tcf(c_15169,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(ordered_pair(X0,apply(sK19(X1),X0)),X1)
| ~ function(sK19(X1))
| ~ relation(sK19(X1))
| ~ in(X0,relation_dom(sK19(X1))) ),
inference(superposition,[status(thm)],[c_87,c_4215]) ).
tcf(c_15170,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| in(sK13(sK19(X0),X1),X1)
| element(ordered_pair(sK14(sK19(X0),X1),sK13(sK19(X0),X1)),X0)
| ( relation_rng(sK19(X0)) = X1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_105,c_4215]) ).
tcf(c_15171,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(ordered_pair(sK15(sK19(X1),X0),X0),X1)
| ~ relation(sK19(X1))
| ~ in(X0,relation_rng(sK19(X1))) ),
inference(superposition,[status(thm)],[c_107,c_4215]) ).
tcf(c_15172,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK22(sK19(X0),X1),sK21(sK19(X0),X1)),X0)
| in(ordered_pair(sK21(sK19(X0),X1),sK22(sK19(X0),X1)),X1)
| ( relation_inverse(sK19(X0)) = X1 )
| ~ relation(X1)
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_125,c_4215]) ).
tcf(c_15173,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK21(X1,sK19(X0)),sK22(X1,sK19(X0))),X0)
| in(ordered_pair(sK22(X1,sK19(X0)),sK21(X1,sK19(X0))),X1)
| ( relation_inverse(X1) = sK19(X0) )
| ~ relation(X1)
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_125,c_4215]) ).
tcf(c_15174,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK23(X1,sK19(X0)),sK24(X1,sK19(X0))),X0)
| in(ordered_pair(sK23(X1,sK19(X0)),sK24(X1,sK19(X0))),X1)
| ( sK19(X0) = X1 )
| ~ relation(X1)
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_130,c_4215]) ).
tcf(c_15175,plain,
! [X0: $i,X1: $i] :
( empty(X0)
| element(ordered_pair(sK23(sK19(X0),X1),sK24(sK19(X0),X1)),X0)
| in(ordered_pair(sK23(sK19(X0),X1),sK24(sK19(X0),X1)),X1)
| ( sK19(X0) = X1 )
| ~ relation(X1)
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_130,c_4215]) ).
tcf(c_15176,plain,
! [X0: $i] :
( empty(X0)
| empty(sK19(X0))
| element(sK20(sK19(X0)),X0) ),
inference(superposition,[status(thm)],[c_3448,c_4215]) ).
tcf(c_15177,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_4215]) ).
tcf(c_15178,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_4215]) ).
tcf(c_15179,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_4215]) ).
tcf(c_15180,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| in(sK5(sK1,sK19(X0)),relation_dom(sK1))
| ( sK19(X0) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8302,c_4215]) ).
tcf(c_15181,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| in(sK6(sK1,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_5335,c_4215]) ).
tcf(c_15182,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK19(X0))) = sK5(sK1,sK19(X0)) ) ),
inference(superposition,[status(thm)],[c_5141,c_4215]) ).
tcf(c_15183,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_4215]) ).
tcf(c_15184,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_4215]) ).
tcf(c_15185,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_4215]) ).
tcf(c_15186,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| in(sK14(sK1,sK19(X0)),relation_dom(sK1))
| ( sK19(X0) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8298,c_4215]) ).
tcf(c_15187,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK19(X0))) = sK14(sK1,sK19(X0)) ) ),
inference(superposition,[status(thm)],[c_5563,c_4215]) ).
tcf(c_15188,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| in(sK13(sK1,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_5542,c_4215]) ).
tcf(c_15189,plain,
! [X0: $i] :
( empty(X0)
| in(sK23(sK19(X0),sK1),relation_dom(sK1))
| element(ordered_pair(sK23(sK19(X0),sK1),sK24(sK19(X0),sK1)),X0)
| ( sK19(X0) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_8327,c_4215]) ).
tcf(c_15190,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK23(sK19(X0),sK1),sK24(sK19(X0),sK1)),X0)
| ( sK19(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK19(X0),sK1)) = sK23(sK19(X0),sK1) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5709,c_4215]) ).
tcf(c_15191,plain,
! [X0: $i] :
( empty(X0)
| in(sK24(sK19(X0),sK1),relation_dom(sK2))
| element(ordered_pair(sK23(sK19(X0),sK1),sK24(sK19(X0),sK1)),X0)
| ( sK19(X0) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5669,c_4215]) ).
tcf(c_15192,plain,
! [X0: $i] :
( empty(X0)
| in(sK23(sK1,sK19(X0)),relation_dom(sK1))
| element(ordered_pair(sK23(sK1,sK19(X0)),sK24(sK1,sK19(X0))),X0)
| ( sK19(X0) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_8322,c_4215]) ).
tcf(c_15193,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK23(sK1,sK19(X0)),sK24(sK1,sK19(X0))),X0)
| ( sK19(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK19(X0))) = sK23(sK1,sK19(X0)) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5704,c_4215]) ).
tcf(c_15194,plain,
! [X0: $i] :
( empty(X0)
| in(sK24(sK1,sK19(X0)),relation_dom(sK2))
| element(ordered_pair(sK23(sK1,sK19(X0)),sK24(sK1,sK19(X0))),X0)
| ( sK19(X0) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5654,c_4215]) ).
tcf(c_15195,plain,
! [X0: $i] :
( empty(X0)
| in(sK21(sK19(X0),sK1),relation_dom(sK1))
| element(ordered_pair(sK22(sK19(X0),sK1),sK21(sK19(X0),sK1)),X0)
| ( relation_inverse(sK19(X0)) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_8332,c_4215]) ).
tcf(c_15196,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK22(sK19(X0),sK1),sK21(sK19(X0),sK1)),X0)
| ( relation_inverse(sK19(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK19(X0),sK1)) = sK21(sK19(X0),sK1) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5969,c_4215]) ).
tcf(c_15197,plain,
! [X0: $i] :
( empty(X0)
| in(sK22(sK19(X0),sK1),relation_dom(sK2))
| element(ordered_pair(sK22(sK19(X0),sK1),sK21(sK19(X0),sK1)),X0)
| ( relation_inverse(sK19(X0)) = sK1 )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5929,c_4215]) ).
tcf(c_15198,plain,
! [X0: $i] :
( empty(X0)
| in(sK22(sK1,sK19(X0)),relation_dom(sK1))
| element(ordered_pair(sK21(sK1,sK19(X0)),sK22(sK1,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK1) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_8337,c_4215]) ).
tcf(c_15199,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK21(sK1,sK19(X0)),sK22(sK1,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK19(X0))) = sK22(sK1,sK19(X0)) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5964,c_4215]) ).
tcf(c_15200,plain,
! [X0: $i] :
( empty(X0)
| in(sK21(sK1,sK19(X0)),relation_dom(sK2))
| element(ordered_pair(sK21(sK1,sK19(X0)),sK22(sK1,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK1) )
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_5914,c_4215]) ).
tcf(c_15201,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(empty_set,sK19(X0)),X0)
| ( sK19(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_8158,c_4215]) ).
tcf(c_15202,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(empty_set,sK19(X0)),X0)
| ( sK19(X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_8154,c_4215]) ).
tcf(c_15626,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_15068,c_70]) ).
tcf(c_15627,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_69]) ).
tcf(c_15628,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_67]) ).
tcf(c_15629,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_12284]) ).
tcf(c_15631,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15068,c_5348]) ).
tcf(c_15632,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_4619]) ).
tcf(c_15633,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_4406]) ).
tcf(c_15634,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_8115]) ).
tcf(c_15640,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_4215]) ).
tcf(c_15641,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_4216]) ).
tcf(c_15642,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_4201]) ).
tcf(c_15643,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_10578]) ).
tcf(c_15681,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(instantiation,[status(thm)],[c_15628]) ).
tcf(c_15693,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_15072,c_70]) ).
tcf(c_15694,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_69]) ).
tcf(c_15695,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_67]) ).
tcf(c_15701,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_8115]) ).
tcf(c_15702,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_12701]) ).
tcf(c_15704,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_10144]) ).
tcf(c_15705,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_8393]) ).
tcf(c_15706,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_4468]) ).
tcf(c_15707,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_4215]) ).
tcf(c_15708,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_4216]) ).
tcf(c_15709,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_4201]) ).
tcf(c_15710,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_12622]) ).
tcf(c_15748,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(instantiation,[status(thm)],[c_15695]) ).
tcf(c_15805,plain,
( ~ empty(relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_15076,c_3684,c_3712]) ).
tcf(c_15806,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(renaming,[status(thm)],[c_15805]) ).
tcf(c_15827,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_6421,c_87]) ).
tcf(c_15828,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6421,c_13488]) ).
tcf(c_15829,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_12807]) ).
tcf(c_15830,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6421,c_4623]) ).
tcf(c_15831,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_4763]) ).
tcf(c_15848,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_15827,c_4030]) ).
tcf(c_15849,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15848,c_987,c_3611]) ).
tcf(c_15878,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11295]) ).
tcf(c_15879,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11295]) ).
tcf(c_15880,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11295]) ).
tcf(c_15881,plain,
relation_dom(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11295]) ).
tcf(c_15882,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11295]) ).
tcf(c_15883,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11295]) ).
tcf(c_15884,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11295]) ).
tcf(c_15885,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11295]) ).
tcf(c_15886,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11295]) ).
tcf(c_15887,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11295]) ).
tcf(c_15896,plain,
( ( relation_dom(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_15882,c_4030]) ).
tcf(c_15915,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11296]) ).
tcf(c_15916,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11296]) ).
tcf(c_15917,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11296]) ).
tcf(c_15918,plain,
relation_dom(relation_dom(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11296]) ).
tcf(c_15919,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11296]) ).
tcf(c_15920,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11296]) ).
tcf(c_15921,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11296]) ).
tcf(c_15922,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11296]) ).
tcf(c_15923,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11296]) ).
tcf(c_15924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11296]) ).
tcf(c_15950,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11297]) ).
tcf(c_15951,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11297]) ).
tcf(c_15952,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11297]) ).
tcf(c_15953,plain,
relation_dom(relation_dom(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11297]) ).
tcf(c_15954,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11297]) ).
tcf(c_15955,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11297]) ).
tcf(c_15956,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11297]) ).
tcf(c_15957,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11297]) ).
tcf(c_15958,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11297]) ).
tcf(c_15959,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11297]) ).
tcf(c_16053,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11658]) ).
tcf(c_16054,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11658]) ).
tcf(c_16055,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11658]) ).
tcf(c_16056,plain,
relation_dom(relation_rng(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11658]) ).
tcf(c_16057,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11658]) ).
tcf(c_16058,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11658]) ).
tcf(c_16059,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11658]) ).
tcf(c_16060,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11658]) ).
tcf(c_16061,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11658]) ).
tcf(c_16062,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11658]) ).
tcf(c_16071,plain,
( ( relation_dom(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_16057,c_4030]) ).
tcf(c_16162,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_89,c_15040]) ).
tcf(c_16163,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_15040]) ).
tcf(c_16164,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_15040]) ).
tcf(c_16165,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_15040]) ).
tcf(c_16166,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_15040]) ).
tcf(c_16167,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_15040]) ).
tcf(c_16168,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_15040]) ).
tcf(c_16169,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_15040]) ).
tcf(c_16170,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_15040]) ).
tcf(c_16171,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_15040]) ).
tcf(c_16180,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_15040]) ).
tcf(c_16185,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5563,c_15040]) ).
tcf(c_16187,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_15040]) ).
tcf(c_16188,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_15040]) ).
tcf(c_16189,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_15040]) ).
tcf(c_16190,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_15040]) ).
tcf(c_16191,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_15040]) ).
tcf(c_16192,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_15040]) ).
tcf(c_16193,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_15040]) ).
tcf(c_16194,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_15040]) ).
tcf(c_16195,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_15040]) ).
tcf(c_16196,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_15040]) ).
tcf(c_16197,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_15040]) ).
tcf(c_16198,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_15040]) ).
tcf(c_16219,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16162,c_65,c_64]) ).
tcf(c_16319,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_89,c_15043]) ).
tcf(c_16320,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_15043]) ).
tcf(c_16321,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_15043]) ).
tcf(c_16322,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_15043]) ).
tcf(c_16323,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_15043]) ).
tcf(c_16324,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_15043]) ).
tcf(c_16325,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_15043]) ).
tcf(c_16326,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_15043]) ).
tcf(c_16327,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_15043]) ).
tcf(c_16328,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_15043]) ).
tcf(c_16330,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4546,c_15043]) ).
tcf(c_16333,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5275,c_15043]) ).
tcf(c_16340,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5141,c_15043]) ).
tcf(c_16352,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_15043]) ).
tcf(c_16353,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_15043]) ).
tcf(c_16354,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_15043]) ).
tcf(c_16355,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_15043]) ).
tcf(c_16356,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_15043]) ).
tcf(c_16357,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_15043]) ).
tcf(c_16358,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_15043]) ).
tcf(c_16359,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_15043]) ).
tcf(c_16360,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_15043]) ).
tcf(c_16361,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_15043]) ).
tcf(c_16362,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_15043]) ).
tcf(c_16363,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_15043]) ).
tcf(c_16381,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16319,c_62,c_61]) ).
tcf(c_16776,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,ordered_pair(sK23(sK1,X0),sK24(sK1,X0))) ),
inference(superposition,[status(thm)],[c_15109,c_70]) ).
tcf(c_16777,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),X0)
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_69]) ).
tcf(c_16778,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_67]) ).
tcf(c_16779,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_106]) ).
tcf(c_16780,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_78]) ).
tcf(c_16781,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(X0,sK23(sK1,X0)) = sK24(sK1,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_197]) ).
tcf(c_16782,plain,
! [X0: $i] :
( in(ordered_pair(sK24(sK1,relation_inverse(X0)),sK23(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_15109,c_297]) ).
tcf(c_16783,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(superposition,[status(thm)],[c_15109,c_129]) ).
tcf(c_16784,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_15040]) ).
tcf(c_16785,plain,
( ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_12284]) ).
tcf(c_16786,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_10726]) ).
tcf(c_16787,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_5348]) ).
tcf(c_16788,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_4619]) ).
tcf(c_16789,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_4406]) ).
tcf(c_16795,plain,
( ( sK1 = empty_set )
| ~ relation(empty_set)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15109,c_8115]) ).
tcf(c_16796,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_15043]) ).
tcf(c_16797,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_12701]) ).
tcf(c_16798,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_10124]) ).
tcf(c_16799,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_10144]) ).
tcf(c_16800,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_8393]) ).
tcf(c_16801,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_4468]) ).
tcf(c_16802,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK23(sK1,sK19(X0)),sK24(sK1,sK19(X0))),X0)
| ( sK19(X0) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_15109,c_4215]) ).
tcf(c_16803,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,sK20(powerset(X0))),sK24(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15109,c_4216]) ).
tcf(c_16804,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15109,c_4201]) ).
tcf(c_16805,plain,
( ( sK1 = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16795,c_135]) ).
tcf(c_16854,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(ordered_pair(sK23(sK1,X0),sK24(sK1,X0)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16783,c_64]) ).
tcf(c_16946,plain,
( ~ empty(relation_rng(sK1))
| ~ in(sK3,relation_rng(sK1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_17020,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,ordered_pair(sK23(X0,sK1),sK24(X0,sK1))) ),
inference(superposition,[status(thm)],[c_15114,c_70]) ).
tcf(c_17021,plain,
! [X0: $i] :
( element(ordered_pair(sK23(X0,sK1),sK24(X0,sK1)),X0)
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_69]) ).
tcf(c_17023,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_106]) ).
tcf(c_17024,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_78]) ).
tcf(c_17025,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(X0,sK23(X0,sK1)) = sK24(X0,sK1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_197]) ).
tcf(c_17026,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(X0),sK1),sK23(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_15114,c_297]) ).
tcf(c_17029,plain,
( ( relation_dom(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_12284]) ).
tcf(c_17032,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_4619]) ).
tcf(c_17033,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15114,c_4406]) ).
tcf(c_17041,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15114,c_12701]) ).
tcf(c_17043,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15114,c_10144]) ).
tcf(c_17045,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15114,c_4468]) ).
tcf(c_17046,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK23(sK19(X0),sK1),sK24(sK19(X0),sK1)),X0)
| ( sK19(X0) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_15114,c_4215]) ).
tcf(c_17047,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK20(powerset(X0)),sK1),sK24(sK20(powerset(X0)),sK1)),X0)
| ( sK20(powerset(X0)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15114,c_4216]) ).
tcf(c_17143,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,ordered_pair(sK22(X0,sK1),sK21(X0,sK1))) ),
inference(superposition,[status(thm)],[c_15119,c_70]) ).
tcf(c_17144,plain,
! [X0: $i] :
( element(ordered_pair(sK22(X0,sK1),sK21(X0,sK1)),X0)
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_69]) ).
tcf(c_17145,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_67]) ).
tcf(c_17146,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_106]) ).
tcf(c_17147,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_78]) ).
tcf(c_17148,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(X0,sK22(X0,sK1)) = sK21(X0,sK1) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_197]) ).
tcf(c_17149,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ relation(sK1)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(superposition,[status(thm)],[c_15119,c_124]) ).
tcf(c_17150,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(X0),sK1),sK22(relation_inverse(X0),sK1)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_15119,c_297]) ).
tcf(c_17151,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_15040]) ).
tcf(c_17152,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_12284]) ).
tcf(c_17153,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_10726]) ).
tcf(c_17154,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_5348]) ).
tcf(c_17155,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_4619]) ).
tcf(c_17156,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_4406]) ).
tcf(c_17157,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_3774]) ).
tcf(c_17162,plain,
( ( relation_inverse(empty_set) = sK1 )
| ~ relation(empty_set)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15119,c_8115]) ).
tcf(c_17163,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_15043]) ).
tcf(c_17164,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_12701]) ).
tcf(c_17165,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_10124]) ).
tcf(c_17166,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_10144]) ).
tcf(c_17167,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_8393]) ).
tcf(c_17168,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_4468]) ).
tcf(c_17169,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK22(sK19(X0),sK1),sK21(sK19(X0),sK1)),X0)
| ( relation_inverse(sK19(X0)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_15119,c_4215]) ).
tcf(c_17170,plain,
! [X0: $i] :
( element(ordered_pair(sK22(sK20(powerset(X0)),sK1),sK21(sK20(powerset(X0)),sK1)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15119,c_4216]) ).
tcf(c_17171,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15119,c_4201]) ).
tcf(c_17221,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(ordered_pair(sK21(X0,sK1),sK22(X0,sK1)),sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17149,c_64]) ).
tcf(c_17315,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,ordered_pair(sK21(sK1,X0),sK22(sK1,X0))) ),
inference(superposition,[status(thm)],[c_15124,c_70]) ).
tcf(c_17316,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,X0),sK22(sK1,X0)),X0)
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_69]) ).
tcf(c_17317,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_67]) ).
tcf(c_17318,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_106]) ).
tcf(c_17319,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_78]) ).
tcf(c_17320,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(X0,sK21(sK1,X0)) = sK22(sK1,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_197]) ).
tcf(c_17321,plain,
! [X0: $i] :
( in(ordered_pair(sK22(sK1,relation_inverse(X0)),sK21(sK1,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK1) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_15124,c_297]) ).
tcf(c_17322,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_15040]) ).
tcf(c_17323,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_12284]) ).
tcf(c_17324,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_10726]) ).
tcf(c_17325,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_5348]) ).
tcf(c_17326,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_4619]) ).
tcf(c_17327,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_4406]) ).
tcf(c_17333,plain,
( ( relation_inverse(sK1) = empty_set )
| ~ relation(empty_set)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15124,c_8115]) ).
tcf(c_17334,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_15043]) ).
tcf(c_17335,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_12701]) ).
tcf(c_17336,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_10124]) ).
tcf(c_17337,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_10144]) ).
tcf(c_17338,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_8393]) ).
tcf(c_17339,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_4468]) ).
tcf(c_17340,plain,
! [X0: $i] :
( empty(X0)
| element(ordered_pair(sK21(sK1,sK19(X0)),sK22(sK1,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_15124,c_4215]) ).
tcf(c_17341,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,sK20(powerset(X0))),sK22(sK1,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15124,c_4216]) ).
tcf(c_17342,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_15124,c_4201]) ).
tcf(c_17343,plain,
( ( relation_inverse(sK1) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17333,c_135]) ).
tcf(c_17543,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11659]) ).
tcf(c_17544,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11659]) ).
tcf(c_17545,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11659]) ).
tcf(c_17546,plain,
relation_dom(relation_rng(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11659]) ).
tcf(c_17547,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11659]) ).
tcf(c_17548,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11659]) ).
tcf(c_17549,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11659]) ).
tcf(c_17550,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11659]) ).
tcf(c_17551,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11659]) ).
tcf(c_17552,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11659]) ).
tcf(c_17578,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11660]) ).
tcf(c_17579,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11660]) ).
tcf(c_17580,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11660]) ).
tcf(c_17581,plain,
relation_dom(relation_rng(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11660]) ).
tcf(c_17582,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11660]) ).
tcf(c_17583,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11660]) ).
tcf(c_17584,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11660]) ).
tcf(c_17585,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11660]) ).
tcf(c_17586,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11660]) ).
tcf(c_17587,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11660]) ).
tcf(c_17622,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11689]) ).
tcf(c_17623,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11689]) ).
tcf(c_17624,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11689]) ).
tcf(c_17625,plain,
relation_dom(relation_inverse(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11689]) ).
tcf(c_17626,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11689]) ).
tcf(c_17627,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11689]) ).
tcf(c_17628,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11689]) ).
tcf(c_17629,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11689]) ).
tcf(c_17630,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11689]) ).
tcf(c_17631,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11689]) ).
tcf(c_17640,plain,
( ( relation_dom(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_17626,c_4030]) ).
tcf(c_17692,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11690]) ).
tcf(c_17693,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11690]) ).
tcf(c_17694,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11690]) ).
tcf(c_17695,plain,
relation_dom(relation_inverse(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11690]) ).
tcf(c_17696,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11690]) ).
tcf(c_17697,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11690]) ).
tcf(c_17698,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11690]) ).
tcf(c_17699,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11690]) ).
tcf(c_17700,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11690]) ).
tcf(c_17701,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11690]) ).
tcf(c_17826,plain,
( ( sK1 = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_16805]) ).
tcf(c_17834,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK2),sK24(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8147,c_70]) ).
tcf(c_17835,plain,
( element(sK24(sK1,empty_set),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_8147,c_69]) ).
tcf(c_17836,plain,
( ( sK1 = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8147,c_67]) ).
tcf(c_17838,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8147,c_12701]) ).
tcf(c_17840,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8147,c_10144]) ).
tcf(c_17841,plain,
( ( sK1 = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8147,c_8393]) ).
tcf(c_17842,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8147,c_4468]) ).
tcf(c_17862,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_16180]) ).
tcf(c_17872,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_15628]) ).
tcf(c_17885,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_16784,c_3712,c_15748]) ).
tcf(c_17891,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_17885]) ).
tcf(c_17892,plain,
( ( relation_dom(sK1) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_17885]) ).
tcf(c_17897,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_16796,c_3712,c_15681]) ).
tcf(c_17903,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_17897]) ).
tcf(c_17904,plain,
( ( relation_dom(sK2) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_17897]) ).
tcf(c_17916,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_15627,c_114]) ).
tcf(c_17917,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = relation_dom(sK2) )
| ~ empty(X1)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_15627,c_113]) ).
tcf(c_17952,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_15642]) ).
tcf(c_17967,plain,
( in(ordered_pair(sK21(sK1,sK1),sK15(sK1,sK21(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_7060,c_87]) ).
tcf(c_17968,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7060,c_13488]) ).
tcf(c_17969,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_12807]) ).
tcf(c_17970,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7060,c_4623]) ).
tcf(c_17971,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_7472]) ).
tcf(c_17987,plain,
( in(ordered_pair(sK21(sK1,sK1),sK15(sK1,sK21(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_17967,c_4030]) ).
tcf(c_17988,plain,
( in(ordered_pair(sK21(sK1,sK1),sK15(sK1,sK21(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17987,c_987,c_3611]) ).
tcf(c_18055,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11691]) ).
tcf(c_18056,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11691]) ).
tcf(c_18057,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11691]) ).
tcf(c_18058,plain,
relation_dom(relation_inverse(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11691]) ).
tcf(c_18059,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11691]) ).
tcf(c_18060,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11691]) ).
tcf(c_18061,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11691]) ).
tcf(c_18062,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11691]) ).
tcf(c_18063,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11691]) ).
tcf(c_18064,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11691]) ).
tcf(c_18130,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ( powerset(X1) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_15694,c_114]) ).
tcf(c_18131,plain,
! [X0: $i,X1: $i] :
( ( powerset(X1) = relation_dom(sK1) )
| ~ empty(X1)
| ~ empty(relation_inverse(sK1))
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_15694,c_113]) ).
tcf(c_18151,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_15709]) ).
tcf(c_18156,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_16778,c_94,c_16778]) ).
tcf(c_18164,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18156]) ).
tcf(c_18165,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_18156]) ).
tcf(c_18172,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17151,c_4146,c_17151]) ).
tcf(c_18178,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_18172]) ).
tcf(c_18179,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_18172]) ).
tcf(c_18204,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17163,c_9854,c_17163]) ).
tcf(c_18210,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_18204]) ).
tcf(c_18211,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_18204]) ).
tcf(c_18216,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17322,c_4146,c_17322]) ).
tcf(c_18222,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_18216]) ).
tcf(c_18223,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_18216]) ).
tcf(c_18280,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17334,c_9854,c_17334]) ).
tcf(c_18286,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_18280]) ).
tcf(c_18287,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_18280]) ).
tcf(c_18303,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_7241,c_87]) ).
tcf(c_18304,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7241,c_13488]) ).
tcf(c_18305,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_12807]) ).
tcf(c_18306,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7241,c_4623]) ).
tcf(c_18307,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_4763]) ).
tcf(c_18325,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_18303,c_4030]) ).
tcf(c_18326,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18325,c_987,c_3611]) ).
tcf(c_18395,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17145,c_94,c_17145]) ).
tcf(c_18403,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18395]) ).
tcf(c_18404,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_18395]) ).
tcf(c_18411,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_17317,c_94,c_17317]) ).
tcf(c_18419,plain,
! [X0: $i,X1: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X1,X0),sK2)
| ~ in(relation_inverse(sK2),ordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_3696,c_70]) ).
tcf(c_18420,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X1,X0),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_69]) ).
tcf(c_18421,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_67]) ).
tcf(c_18422,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK2)) = X1 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(relation_inverse(sK2),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK2),X1)),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_76]) ).
tcf(c_18423,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_inverse(sK2)))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_106]) ).
tcf(c_18424,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(relation_inverse(sK2)))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_78]) ).
tcf(c_18425,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK2),X1) = X0 )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_197]) ).
tcf(c_18426,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK2)) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(relation_inverse(sK2),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK2),X0),X1),sK2) ),
inference(superposition,[status(thm)],[c_3696,c_104]) ).
tcf(c_18427,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK2)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),sK2)
| ~ in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),X0) ),
inference(superposition,[status(thm)],[c_3696,c_124]) ).
tcf(c_18429,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK24(X0,relation_inverse(sK2)),sK23(X0,relation_inverse(sK2))),sK2)
| ~ in(ordered_pair(sK23(X0,relation_inverse(sK2)),sK24(X0,relation_inverse(sK2))),X0) ),
inference(superposition,[status(thm)],[c_3696,c_129]) ).
tcf(c_18433,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(light_normalisation,[status(thm)],[c_18424,c_3805]) ).
tcf(c_18437,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(X0,X1),sK2) ),
inference(light_normalisation,[status(thm)],[c_18423,c_3845]) ).
tcf(c_18451,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(relation_inverse(sK2),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK2),X0),X1),sK2) ),
inference(light_normalisation,[status(thm)],[c_18426,c_3845]) ).
tcf(c_18456,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK2) = X1 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(relation_inverse(sK2),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK2),X1)),sK2) ),
inference(light_normalisation,[status(thm)],[c_18422,c_3805]) ).
tcf(c_18466,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),sK2)
| ~ in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),X0) ),
inference(light_normalisation,[status(thm)],[c_18427,c_3624]) ).
tcf(c_18694,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_18433]) ).
tcf(c_18695,plain,
! [X0: $i] :
( in(sK7(sK2,X0),relation_rng(sK2))
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_79,c_18433]) ).
tcf(c_18696,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_rng(sK2))
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_87,c_18433]) ).
tcf(c_18697,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_18433]) ).
tcf(c_18699,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| in(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_18433]) ).
tcf(c_18700,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| in(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_18433]) ).
tcf(c_18701,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| in(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_18433]) ).
tcf(c_18702,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_18433]) ).
tcf(c_18703,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15114,c_18433]) ).
tcf(c_18704,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_18433]) ).
tcf(c_18705,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_18433]) ).
tcf(c_18706,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_18433]) ).
tcf(c_18707,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_18433]) ).
tcf(c_18708,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_18433]) ).
tcf(c_18709,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_18433]) ).
tcf(c_18710,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_18433]) ).
tcf(c_18711,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_18433]) ).
tcf(c_18712,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_18433]) ).
tcf(c_18713,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_18433]) ).
tcf(c_18714,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_18433]) ).
tcf(c_18715,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_18433]) ).
tcf(c_18716,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_18433]) ).
tcf(c_18717,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_18433]) ).
tcf(c_18718,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_18433]) ).
tcf(c_18719,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11421,c_18433]) ).
tcf(c_18720,plain,
! [X0: $i] :
( in(sK7(sK2,X0),relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18695,c_61]) ).
tcf(c_18724,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18707,c_61]) ).
tcf(c_18729,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18703,c_61]) ).
tcf(c_18734,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18696,c_62,c_61]) ).
tcf(c_18738,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18715,c_61]) ).
tcf(c_18743,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18711,c_61]) ).
tcf(c_18748,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18710,c_61]) ).
tcf(c_18753,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18708,c_61]) ).
tcf(c_18758,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18706,c_61]) ).
tcf(c_18763,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18704,c_61]) ).
tcf(c_18768,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18697,c_61]) ).
tcf(c_18773,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18694,c_61]) ).
tcf(c_18778,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18718,c_61]) ).
tcf(c_18783,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18716,c_61]) ).
tcf(c_18788,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18714,c_61]) ).
tcf(c_18793,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18712,c_61]) ).
tcf(c_18798,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18709,c_61]) ).
tcf(c_18803,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18705,c_61]) ).
tcf(c_18813,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18717,c_61]) ).
tcf(c_18818,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18713,c_61]) ).
tcf(c_18823,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18702,c_61]) ).
tcf(c_18829,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| in(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18701,c_61]) ).
tcf(c_18835,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| in(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18700,c_61]) ).
tcf(c_18841,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| in(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18699,c_61]) ).
tcf(c_18885,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11727]) ).
tcf(c_18886,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11727]) ).
tcf(c_18887,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11727]) ).
tcf(c_18888,plain,
relation_rng(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11727]) ).
tcf(c_18889,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11727]) ).
tcf(c_18890,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11727]) ).
tcf(c_18891,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11727]) ).
tcf(c_18892,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11727]) ).
tcf(c_18893,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11727]) ).
tcf(c_18894,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11727]) ).
tcf(c_18903,plain,
( ( relation_rng(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_18889,c_4030]) ).
tcf(c_18931,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11728]) ).
tcf(c_18932,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11728]) ).
tcf(c_18933,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11728]) ).
tcf(c_18934,plain,
relation_rng(relation_dom(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11728]) ).
tcf(c_18935,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11728]) ).
tcf(c_18936,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11728]) ).
tcf(c_18937,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11728]) ).
tcf(c_18938,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11728]) ).
tcf(c_18939,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11728]) ).
tcf(c_18940,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11728]) ).
tcf(c_18984,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11729]) ).
tcf(c_18985,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11729]) ).
tcf(c_18986,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11729]) ).
tcf(c_18987,plain,
relation_rng(relation_dom(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11729]) ).
tcf(c_18988,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11729]) ).
tcf(c_18989,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11729]) ).
tcf(c_18990,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11729]) ).
tcf(c_18991,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11729]) ).
tcf(c_18992,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11729]) ).
tcf(c_18993,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11729]) ).
tcf(c_19042,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11769]) ).
tcf(c_19043,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11769]) ).
tcf(c_19044,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11769]) ).
tcf(c_19045,plain,
relation_rng(relation_rng(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11769]) ).
tcf(c_19046,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11769]) ).
tcf(c_19047,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11769]) ).
tcf(c_19048,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11769]) ).
tcf(c_19049,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11769]) ).
tcf(c_19050,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11769]) ).
tcf(c_19051,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11769]) ).
tcf(c_19060,plain,
( ( relation_rng(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_19046,c_4030]) ).
tcf(c_19093,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK2),sK24(empty_set,sK1)) ),
inference(superposition,[status(thm)],[c_8150,c_70]) ).
tcf(c_19094,plain,
( element(sK24(empty_set,sK1),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_8150,c_69]) ).
tcf(c_19097,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8150,c_12701]) ).
tcf(c_19099,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8150,c_10144]) ).
tcf(c_19101,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8150,c_4468]) ).
tcf(c_19125,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK1),sK23(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_8873,c_70]) ).
tcf(c_19126,plain,
( element(sK23(sK1,empty_set),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_8873,c_69]) ).
tcf(c_19129,plain,
( ( sK1 = empty_set )
| ( sK15(relation_inverse(sK1),sK23(sK1,empty_set)) = apply(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8873,c_12284]) ).
tcf(c_19132,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8873,c_4619]) ).
tcf(c_19133,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8873,c_4406]) ).
tcf(c_19168,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK1),sK23(empty_set,sK1)) ),
inference(superposition,[status(thm)],[c_8992,c_70]) ).
tcf(c_19169,plain,
( element(sK23(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_8992,c_69]) ).
tcf(c_19172,plain,
( ( sK1 = empty_set )
| ( sK15(relation_inverse(sK1),sK23(empty_set,sK1)) = apply(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8992,c_12284]) ).
tcf(c_19175,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8992,c_4619]) ).
tcf(c_19176,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8992,c_4406]) ).
tcf(c_19284,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK1),sK21(empty_set,sK1)) ),
inference(superposition,[status(thm)],[c_9083,c_70]) ).
tcf(c_19285,plain,
( element(sK21(empty_set,sK1),relation_dom(sK1))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_9083,c_69]) ).
tcf(c_19288,plain,
( ( sK1 = empty_set )
| ( sK15(relation_inverse(sK1),sK21(empty_set,sK1)) = apply(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_9083,c_12284]) ).
tcf(c_19291,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_9083,c_4619]) ).
tcf(c_19292,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_9083,c_4406]) ).
tcf(c_19373,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2))
| ~ in(relation_rng(sK2),sK7(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18720,c_70]) ).
tcf(c_19374,plain,
! [X0: $i] :
( element(sK7(sK2,X0),relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_69]) ).
tcf(c_19375,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_67]) ).
tcf(c_19430,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2))
| ~ in(relation_rng(sK2),apply(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18734,c_70]) ).
tcf(c_19431,plain,
! [X0: $i] :
( element(apply(sK2,X0),relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18734,c_69]) ).
tcf(c_19441,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_18724,c_3712,c_9882,c_18724]) ).
tcf(c_19449,plain,
( ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ in(relation_rng(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_19441,c_70]) ).
tcf(c_19450,plain,
( element(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_19441,c_69]) ).
tcf(c_19451,plain,
( ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_19441,c_67]) ).
tcf(c_19495,plain,
( ~ empty(relation_inverse(sK1))
| ( sK1 = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_18729,c_3712,c_9887,c_19451]) ).
tcf(c_19496,plain,
( ( sK1 = sK2 )
| ~ empty(relation_inverse(sK1)) ),
inference(renaming,[status(thm)],[c_19495]) ).
tcf(c_19501,plain,
( ( sK1 = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_19496]) ).
tcf(c_19502,plain,
( ( sK1 = sK2 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_19496]) ).
tcf(c_19507,plain,
( ~ empty(relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 ) ),
inference(global_subsumption_just,[status(thm)],[c_18738,c_4147,c_13837]) ).
tcf(c_19508,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_inverse(sK1)) ),
inference(renaming,[status(thm)],[c_19507]) ).
tcf(c_19513,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_19508]) ).
tcf(c_19514,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_19508]) ).
tcf(c_19523,plain,
( ~ empty(relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_18743,c_3712,c_9913]) ).
tcf(c_19524,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(renaming,[status(thm)],[c_19523]) ).
tcf(c_19529,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_19524]) ).
tcf(c_19530,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_19524]) ).
tcf(c_19558,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_70]) ).
tcf(c_19559,plain,
( element(sK24(sK1,sK2),relation_rng(sK2))
| in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_69]) ).
tcf(c_19560,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_67]) ).
tcf(c_19581,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18753,c_70]) ).
tcf(c_19582,plain,
( element(sK24(sK1,sK2),relation_rng(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18753,c_69]) ).
tcf(c_19583,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18753,c_67]) ).
tcf(c_19621,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11770]) ).
tcf(c_19622,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11770]) ).
tcf(c_19623,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11770]) ).
tcf(c_19624,plain,
relation_rng(relation_rng(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11770]) ).
tcf(c_19625,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11770]) ).
tcf(c_19626,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11770]) ).
tcf(c_19627,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11770]) ).
tcf(c_19628,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11770]) ).
tcf(c_19629,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11770]) ).
tcf(c_19630,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11770]) ).
tcf(c_19686,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18758,c_70]) ).
tcf(c_19687,plain,
( element(sK24(sK2,sK1),relation_rng(sK2))
| in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18758,c_69]) ).
tcf(c_19688,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18758,c_67]) ).
tcf(c_19711,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18763,c_70]) ).
tcf(c_19712,plain,
( element(sK24(sK2,sK1),relation_rng(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18763,c_69]) ).
tcf(c_19713,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18763,c_67]) ).
tcf(c_19952,plain,
! [X0: $i] :
( in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,sK13(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18768,c_70]) ).
tcf(c_19953,plain,
! [X0: $i] :
( element(sK13(sK2,X0),X0)
| in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_69]) ).
tcf(c_19954,plain,
! [X0: $i] :
( in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_67]) ).
tcf(c_19955,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_15040]) ).
tcf(c_19956,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK13(sK2,relation_dom(sK1))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_12284]) ).
tcf(c_19957,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_10726]) ).
tcf(c_19958,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_5348]) ).
tcf(c_19959,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4619]) ).
tcf(c_19960,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4406]) ).
tcf(c_19961,plain,
( in(sK13(sK2,empty_set),relation_rng(sK2))
| ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_8115]) ).
tcf(c_19962,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_15043]) ).
tcf(c_19963,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_12701]) ).
tcf(c_19964,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_10124]) ).
tcf(c_19965,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_10144]) ).
tcf(c_19966,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_8393]) ).
tcf(c_19967,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK2,relation_dom(sK2))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4468]) ).
tcf(c_19968,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK2,sK19(X0)),X0)
| in(sK13(sK2,sK19(X0)),relation_rng(sK2))
| ( sK19(X0) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4215]) ).
tcf(c_19969,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(powerset(X0))),X0)
| in(sK13(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4216]) ).
tcf(c_19970,plain,
! [X0: $i] :
( in(sK13(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4201]) ).
tcf(c_19971,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK13(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18768,c_70]) ).
tcf(c_19972,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| element(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_69]) ).
tcf(c_19973,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_67]) ).
tcf(c_20111,plain,
! [X0: $i] :
( in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,sK5(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18773,c_70]) ).
tcf(c_20112,plain,
! [X0: $i] :
( element(sK5(sK2,X0),X0)
| in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_69]) ).
tcf(c_20113,plain,
! [X0: $i] :
( in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_67]) ).
tcf(c_20115,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK5(sK2,relation_dom(sK1))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_12284]) ).
tcf(c_20118,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4619]) ).
tcf(c_20119,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4406]) ).
tcf(c_20120,plain,
( in(sK6(sK2,empty_set),relation_rng(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_8115]) ).
tcf(c_20127,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK2,sK19(X0)),X0)
| in(sK6(sK2,sK19(X0)),relation_rng(sK2))
| ( sK19(X0) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4215]) ).
tcf(c_20128,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(powerset(X0))),X0)
| in(sK6(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4216]) ).
tcf(c_20129,plain,
! [X0: $i] :
( in(sK6(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4201]) ).
tcf(c_20130,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK6(sK2,X0)) ),
inference(superposition,[status(thm)],[c_18773,c_70]) ).
tcf(c_20131,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| element(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_69]) ).
tcf(c_20132,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_67]) ).
tcf(c_20244,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK21(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_70]) ).
tcf(c_20245,plain,
( element(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_69]) ).
tcf(c_20246,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_67]) ).
tcf(c_20248,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_12701]) ).
tcf(c_20250,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_10144]) ).
tcf(c_20251,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_8393]) ).
tcf(c_20252,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK15(sK1,sK21(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_4468]) ).
tcf(c_20299,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK22(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18783,c_70]) ).
tcf(c_20300,plain,
( element(sK22(sK1,sK2),relation_rng(sK2))
| in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18783,c_69]) ).
tcf(c_20301,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18783,c_67]) ).
tcf(c_20333,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK21(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18788,c_70]) ).
tcf(c_20334,plain,
( element(sK21(sK2,sK1),relation_rng(sK2))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18788,c_69]) ).
tcf(c_20335,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18788,c_67]) ).
tcf(c_20367,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK21(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18793,c_70]) ).
tcf(c_20368,plain,
( element(sK21(sK2,sK1),relation_rng(sK2))
| in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18793,c_69]) ).
tcf(c_20369,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18793,c_67]) ).
tcf(c_20402,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK1) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8129,c_87]) ).
tcf(c_20403,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ( relation_dom(sK1) = empty_set )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8129,c_13488]) ).
tcf(c_20404,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8129,c_12807]) ).
tcf(c_20405,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ( relation_dom(sK1) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8129,c_4623]) ).
tcf(c_20406,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(sK1,sK6(sK1,empty_set)) = sK5(sK1,empty_set) )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8129,c_4763]) ).
tcf(c_20419,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK1) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_20402,c_4030]) ).
tcf(c_20420,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK1) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20419,c_987,c_3611]) ).
tcf(c_20565,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11771]) ).
tcf(c_20566,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11771]) ).
tcf(c_20567,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11771]) ).
tcf(c_20568,plain,
relation_rng(relation_rng(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11771]) ).
tcf(c_20569,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11771]) ).
tcf(c_20570,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11771]) ).
tcf(c_20571,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11771]) ).
tcf(c_20572,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11771]) ).
tcf(c_20573,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11771]) ).
tcf(c_20574,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11771]) ).
tcf(c_20731,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11809]) ).
tcf(c_20732,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11809]) ).
tcf(c_20733,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11809]) ).
tcf(c_20734,plain,
relation_rng(relation_inverse(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11809]) ).
tcf(c_20735,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11809]) ).
tcf(c_20736,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11809]) ).
tcf(c_20737,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11809]) ).
tcf(c_20738,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11809]) ).
tcf(c_20739,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11809]) ).
tcf(c_20740,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11809]) ).
tcf(c_20749,plain,
( ( relation_rng(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_20735,c_4030]) ).
tcf(c_20788,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11810]) ).
tcf(c_20789,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11810]) ).
tcf(c_20790,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11810]) ).
tcf(c_20791,plain,
relation_rng(relation_inverse(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11810]) ).
tcf(c_20792,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11810]) ).
tcf(c_20793,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11810]) ).
tcf(c_20794,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11810]) ).
tcf(c_20795,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11810]) ).
tcf(c_20796,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11810]) ).
tcf(c_20797,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11810]) ).
tcf(c_21077,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11811]) ).
tcf(c_21078,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11811]) ).
tcf(c_21079,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11811]) ).
tcf(c_21080,plain,
relation_rng(relation_inverse(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_11811]) ).
tcf(c_21081,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_11811]) ).
tcf(c_21082,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_11811]) ).
tcf(c_21083,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_11811]) ).
tcf(c_21084,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_11811]) ).
tcf(c_21085,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_11811]) ).
tcf(c_21086,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11811]) ).
tcf(c_21198,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18798,c_70]) ).
tcf(c_21199,plain,
( element(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18798,c_69]) ).
tcf(c_21200,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18798,c_67]) ).
tcf(c_21221,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18803,c_70]) ).
tcf(c_21222,plain,
( element(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18803,c_69]) ).
tcf(c_21223,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18803,c_67]) ).
tcf(c_21244,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK22(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_70]) ).
tcf(c_21245,plain,
( element(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_69]) ).
tcf(c_21246,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_67]) ).
tcf(c_21267,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK21(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_18818,c_70]) ).
tcf(c_21268,plain,
( element(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_69]) ).
tcf(c_21269,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_67]) ).
tcf(c_21292,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK23(sK2,X0),sK24(sK2,X0))) ),
inference(superposition,[status(thm)],[c_18823,c_70]) ).
tcf(c_21293,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| element(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_69]) ).
tcf(c_21294,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| ( X0 = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_67]) ).
tcf(c_21295,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| in(sK24(sK2,X0),relation_rng(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_106]) ).
tcf(c_21296,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| in(sK23(sK2,X0),relation_dom(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_78]) ).
tcf(c_21297,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| ( X0 = sK2 )
| ( apply(X0,sK23(sK2,X0)) = sK24(sK2,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_197]) ).
tcf(c_21298,plain,
! [X0: $i] :
( in(sK24(sK2,relation_inverse(X0)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(X0)),sK23(sK2,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_18823,c_297]) ).
tcf(c_21299,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),sK2) ),
inference(superposition,[status(thm)],[c_18823,c_129]) ).
tcf(c_21300,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_15040]) ).
tcf(c_21301,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_12284]) ).
tcf(c_21302,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_10726]) ).
tcf(c_21303,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_5348]) ).
tcf(c_21304,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_4619]) ).
tcf(c_21305,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_4406]) ).
tcf(c_21307,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_3774]) ).
tcf(c_21308,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_4259]) ).
tcf(c_21309,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_4237]) ).
tcf(c_21310,plain,
( in(sK24(sK2,sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_3784]) ).
tcf(c_21311,plain,
( in(sK24(sK2,relation_inverse(sK1)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK1)),sK23(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_3719]) ).
tcf(c_21312,plain,
( in(sK24(sK2,empty_set),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_8115]) ).
tcf(c_21313,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_15043]) ).
tcf(c_21314,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_12701]) ).
tcf(c_21315,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_10124]) ).
tcf(c_21316,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_10144]) ).
tcf(c_21317,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_8393]) ).
tcf(c_21318,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_4468]) ).
tcf(c_21319,plain,
! [X0: $i] :
( empty(X0)
| in(sK24(sK2,sK19(X0)),relation_rng(sK2))
| element(ordered_pair(sK23(sK2,sK19(X0)),sK24(sK2,sK19(X0))),X0)
| ( sK19(X0) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_18823,c_4215]) ).
tcf(c_21320,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(powerset(X0))),relation_rng(sK2))
| element(ordered_pair(sK23(sK2,sK20(powerset(X0))),sK24(sK2,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18823,c_4216]) ).
tcf(c_21321,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18823,c_4201]) ).
tcf(c_21322,plain,
( in(sK24(sK2,empty_set),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21312,c_135]) ).
tcf(c_21390,plain,
! [X0: $i] :
( in(sK24(sK2,X0),relation_rng(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21299,c_61]) ).
tcf(c_21402,plain,
( in(sK24(sK2,relation_inverse(sK1)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK1)),sK23(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21311,c_3611]) ).
tcf(c_21522,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK23(X0,sK2),sK24(X0,sK2))) ),
inference(superposition,[status(thm)],[c_18829,c_70]) ).
tcf(c_21523,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| element(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_69]) ).
tcf(c_21524,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| ( X0 = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_67]) ).
tcf(c_21525,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| in(sK24(X0,sK2),relation_rng(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_106]) ).
tcf(c_21526,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| in(sK23(X0,sK2),relation_dom(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_78]) ).
tcf(c_21527,plain,
! [X0: $i] :
( in(sK24(X0,sK2),relation_rng(sK2))
| ( X0 = sK2 )
| ( apply(X0,sK23(X0,sK2)) = sK24(X0,sK2) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_197]) ).
tcf(c_21528,plain,
! [X0: $i] :
( in(sK24(relation_inverse(X0),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(X0),sK2),sK23(relation_inverse(X0),sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_18829,c_297]) ).
tcf(c_21530,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_15040]) ).
tcf(c_21531,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_12284]) ).
tcf(c_21532,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_10726]) ).
tcf(c_21533,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_5348]) ).
tcf(c_21534,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_4619]) ).
tcf(c_21535,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_4406]) ).
tcf(c_21537,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_3774]) ).
tcf(c_21538,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_4259]) ).
tcf(c_21539,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_4237]) ).
tcf(c_21540,plain,
( in(sK24(sK1,sK2),relation_rng(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_3784]) ).
tcf(c_21541,plain,
( in(sK24(relation_inverse(sK1),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK2),sK23(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_3719]) ).
tcf(c_21542,plain,
( in(sK24(empty_set,sK2),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_8115]) ).
tcf(c_21543,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_15043]) ).
tcf(c_21544,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_12701]) ).
tcf(c_21545,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_10124]) ).
tcf(c_21546,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_10144]) ).
tcf(c_21547,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_8393]) ).
tcf(c_21548,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_4468]) ).
tcf(c_21549,plain,
! [X0: $i] :
( empty(X0)
| in(sK24(sK19(X0),sK2),relation_rng(sK2))
| element(ordered_pair(sK23(sK19(X0),sK2),sK24(sK19(X0),sK2)),X0)
| ( sK19(X0) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_18829,c_4215]) ).
tcf(c_21550,plain,
! [X0: $i] :
( in(sK24(sK20(powerset(X0)),sK2),relation_rng(sK2))
| element(ordered_pair(sK23(sK20(powerset(X0)),sK2),sK24(sK20(powerset(X0)),sK2)),X0)
| ( sK20(powerset(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18829,c_4216]) ).
tcf(c_21551,plain,
! [X0: $i] :
( in(sK24(sK20(powerset(X0)),sK2),relation_rng(sK2))
| ( sK20(powerset(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18829,c_4201]) ).
tcf(c_21552,plain,
( in(sK24(empty_set,sK2),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21542,c_135]) ).
tcf(c_21626,plain,
( in(sK24(relation_inverse(sK1),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK2),sK23(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21541,c_3611]) ).
tcf(c_21786,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK22(X0,sK2),sK21(X0,sK2))) ),
inference(superposition,[status(thm)],[c_18835,c_70]) ).
tcf(c_21787,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| element(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_69]) ).
tcf(c_21788,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_67]) ).
tcf(c_21789,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| in(sK21(X0,sK2),relation_rng(X0))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_106]) ).
tcf(c_21790,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| in(sK22(X0,sK2),relation_dom(X0))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_78]) ).
tcf(c_21791,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| ( relation_inverse(X0) = sK2 )
| ( apply(X0,sK22(X0,sK2)) = sK21(X0,sK2) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_197]) ).
tcf(c_21792,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(X0,sK2),sK22(X0,sK2)),sK2) ),
inference(superposition,[status(thm)],[c_18835,c_124]) ).
tcf(c_21793,plain,
! [X0: $i] :
( in(sK22(relation_inverse(X0),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(X0),sK2),sK22(relation_inverse(X0),sK2)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_18835,c_297]) ).
tcf(c_21794,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_15040]) ).
tcf(c_21795,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_12284]) ).
tcf(c_21796,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_10726]) ).
tcf(c_21797,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_5348]) ).
tcf(c_21798,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_4619]) ).
tcf(c_21799,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_4406]) ).
tcf(c_21800,plain,
( in(sK21(sK2,sK2),relation_rng(sK2))
| in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_18433]) ).
tcf(c_21801,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_3774]) ).
tcf(c_21802,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_4259]) ).
tcf(c_21803,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_4237]) ).
tcf(c_21804,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_3784]) ).
tcf(c_21805,plain,
( in(sK22(relation_inverse(sK1),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(relation_inverse(sK1)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_3719]) ).
tcf(c_21806,plain,
( in(sK22(empty_set,sK2),relation_rng(sK2))
| ( relation_inverse(empty_set) = sK2 )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_8115]) ).
tcf(c_21807,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_15043]) ).
tcf(c_21808,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_12701]) ).
tcf(c_21809,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_10124]) ).
tcf(c_21810,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_10144]) ).
tcf(c_21811,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_8393]) ).
tcf(c_21812,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_4468]) ).
tcf(c_21813,plain,
! [X0: $i] :
( empty(X0)
| in(sK22(sK19(X0),sK2),relation_rng(sK2))
| element(ordered_pair(sK22(sK19(X0),sK2),sK21(sK19(X0),sK2)),X0)
| ( relation_inverse(sK19(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_18835,c_4215]) ).
tcf(c_21814,plain,
! [X0: $i] :
( in(sK22(sK20(powerset(X0)),sK2),relation_rng(sK2))
| element(ordered_pair(sK22(sK20(powerset(X0)),sK2),sK21(sK20(powerset(X0)),sK2)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18835,c_4216]) ).
tcf(c_21815,plain,
! [X0: $i] :
( in(sK22(sK20(powerset(X0)),sK2),relation_rng(sK2))
| ( relation_inverse(sK20(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18835,c_4201]) ).
tcf(c_21816,plain,
( in(sK22(empty_set,sK2),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_21806,c_8232]) ).
tcf(c_21817,plain,
( in(sK22(empty_set,sK2),relation_rng(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21816,c_135]) ).
tcf(c_21834,plain,
( in(sK21(sK2,sK2),relation_rng(sK2))
| in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21800,c_61]) ).
tcf(c_21890,plain,
! [X0: $i] :
( in(sK22(X0,sK2),relation_rng(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(X0,sK2),sK22(X0,sK2)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21792,c_61]) ).
tcf(c_21902,plain,
( in(sK22(relation_inverse(sK1),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_21805,c_3625]) ).
tcf(c_21903,plain,
( in(sK22(relation_inverse(sK1),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21902,c_3611]) ).
tcf(c_22063,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK21(sK2,sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_70]) ).
tcf(c_22064,plain,
( element(sK21(sK2,sK2),relation_rng(sK2))
| in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_69]) ).
tcf(c_22065,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_67]) ).
tcf(c_22097,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8130,c_87]) ).
tcf(c_22098,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8130,c_13488]) ).
tcf(c_22099,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8130,c_12807]) ).
tcf(c_22100,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8130,c_4623]) ).
tcf(c_22101,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,sK13(sK1,empty_set)) = sK14(sK1,empty_set) )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8130,c_4763]) ).
tcf(c_22114,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_22097,c_4030]) ).
tcf(c_22115,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22114,c_987,c_3611]) ).
tcf(c_22303,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14068]) ).
tcf(c_22304,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14068]) ).
tcf(c_22305,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14068]) ).
tcf(c_22306,plain,
relation_inverse(relation_dom(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14068]) ).
tcf(c_22307,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14068]) ).
tcf(c_22308,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14068]) ).
tcf(c_22309,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14068]) ).
tcf(c_22310,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14068]) ).
tcf(c_22311,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14068]) ).
tcf(c_22312,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14068]) ).
tcf(c_22321,plain,
( ( relation_inverse(relation_dom(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_22307,c_4030]) ).
tcf(c_22416,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK21(sK2,X0),sK22(sK2,X0))) ),
inference(superposition,[status(thm)],[c_18841,c_70]) ).
tcf(c_22417,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| element(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_69]) ).
tcf(c_22418,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| ( relation_inverse(sK2) = X0 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_67]) ).
tcf(c_22419,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| in(sK22(sK2,X0),relation_rng(X0))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_106]) ).
tcf(c_22420,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| in(sK21(sK2,X0),relation_dom(X0))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_78]) ).
tcf(c_22421,plain,
! [X0: $i] :
( in(sK21(sK2,X0),relation_rng(sK2))
| ( relation_inverse(sK2) = X0 )
| ( apply(X0,sK21(sK2,X0)) = sK22(sK2,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_197]) ).
tcf(c_22422,plain,
! [X0: $i] :
( in(sK21(sK2,relation_inverse(X0)),relation_rng(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(X0)),sK21(sK2,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK2) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_18841,c_297]) ).
tcf(c_22423,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_15040]) ).
tcf(c_22424,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_12284]) ).
tcf(c_22425,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_10726]) ).
tcf(c_22426,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_5348]) ).
tcf(c_22427,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_4619]) ).
tcf(c_22428,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_4406]) ).
tcf(c_22430,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_3774]) ).
tcf(c_22431,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_4259]) ).
tcf(c_22432,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_4237]) ).
tcf(c_22433,plain,
( in(sK21(sK2,sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_3784]) ).
tcf(c_22434,plain,
( in(sK21(sK2,relation_inverse(sK1)),relation_rng(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK1)),sK21(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_3719]) ).
tcf(c_22435,plain,
( in(sK21(sK2,empty_set),relation_rng(sK2))
| ( relation_inverse(sK2) = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_8115]) ).
tcf(c_22436,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_15043]) ).
tcf(c_22437,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_12701]) ).
tcf(c_22438,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_10124]) ).
tcf(c_22439,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_10144]) ).
tcf(c_22440,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_8393]) ).
tcf(c_22441,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_4468]) ).
tcf(c_22442,plain,
! [X0: $i] :
( empty(X0)
| in(sK21(sK2,sK19(X0)),relation_rng(sK2))
| element(ordered_pair(sK21(sK2,sK19(X0)),sK22(sK2,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_18841,c_4215]) ).
tcf(c_22443,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(powerset(X0))),relation_rng(sK2))
| element(ordered_pair(sK21(sK2,sK20(powerset(X0))),sK22(sK2,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18841,c_4216]) ).
tcf(c_22444,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(powerset(X0))),relation_rng(sK2))
| ( sK20(powerset(X0)) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_18841,c_4201]) ).
tcf(c_22445,plain,
( in(sK21(sK2,empty_set),relation_rng(sK2))
| ( relation_inverse(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22435,c_135]) ).
tcf(c_22519,plain,
( in(sK21(sK2,relation_inverse(sK1)),relation_rng(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK1)),sK21(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22434,c_3611]) ).
tcf(c_22656,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_19375,c_4108,c_8394,c_9676]) ).
tcf(c_22663,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_89,c_22656]) ).
tcf(c_22664,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_22656]) ).
tcf(c_22665,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_22656]) ).
tcf(c_22666,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_22656]) ).
tcf(c_22667,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_22656]) ).
tcf(c_22668,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_22656]) ).
tcf(c_22669,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_22656]) ).
tcf(c_22670,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_22656]) ).
tcf(c_22671,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_22656]) ).
tcf(c_22672,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_22656]) ).
tcf(c_22673,plain,
( empty(relation_dom(sK2))
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_22656]) ).
tcf(c_22674,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_22656]) ).
tcf(c_22675,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_22656]) ).
tcf(c_22677,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5275,c_22656]) ).
tcf(c_22682,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8302,c_22656]) ).
tcf(c_22683,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_22656]) ).
tcf(c_22684,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5141,c_22656]) ).
tcf(c_22685,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_6281,c_22656]) ).
tcf(c_22686,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_22656]) ).
tcf(c_22694,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_6331,c_22656]) ).
tcf(c_22695,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_22656]) ).
tcf(c_22697,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_22656]) ).
tcf(c_22698,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_22656]) ).
tcf(c_22699,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_22656]) ).
tcf(c_22701,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_22656]) ).
tcf(c_22702,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_22656]) ).
tcf(c_22703,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_22656]) ).
tcf(c_22705,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_22656]) ).
tcf(c_22706,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_22656]) ).
tcf(c_22707,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_22656]) ).
tcf(c_22709,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_22656]) ).
tcf(c_22710,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_22656]) ).
tcf(c_22711,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_22656]) ).
tcf(c_22712,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8310,c_22656]) ).
tcf(c_22713,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_7149,c_22656]) ).
tcf(c_22714,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8306,c_22656]) ).
tcf(c_22715,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_6706,c_22656]) ).
tcf(c_22716,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_6686,c_22656]) ).
tcf(c_22719,plain,
( ( relation_dom(sK1) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8128,c_22656]) ).
tcf(c_22720,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8131,c_22656]) ).
tcf(c_22721,plain,
( ( sK1 = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8150,c_22656]) ).
tcf(c_22723,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_22656]) ).
tcf(c_22725,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_22656]) ).
tcf(c_22726,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_22656]) ).
tcf(c_22727,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_22656]) ).
tcf(c_22728,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_22656]) ).
tcf(c_22729,plain,
( in(sK22(sK1,sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18778,c_22656]) ).
tcf(c_22769,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22663,c_62,c_61]) ).
tcf(c_23058,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_89,c_22675]) ).
tcf(c_23059,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_22675]) ).
tcf(c_23060,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_22675]) ).
tcf(c_23061,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_22675]) ).
tcf(c_23062,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_22675]) ).
tcf(c_23063,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_22675]) ).
tcf(c_23064,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_22675]) ).
tcf(c_23065,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_22675]) ).
tcf(c_23066,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_22675]) ).
tcf(c_23067,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_22675]) ).
tcf(c_23068,plain,
( empty(relation_dom(sK1))
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_22675]) ).
tcf(c_23080,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8298,c_22675]) ).
tcf(c_23081,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5563,c_22675]) ).
tcf(c_23082,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_22675]) ).
tcf(c_23084,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_22675]) ).
tcf(c_23085,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_22675]) ).
tcf(c_23086,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_22675]) ).
tcf(c_23088,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_22675]) ).
tcf(c_23089,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_22675]) ).
tcf(c_23090,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_22675]) ).
tcf(c_23092,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_22675]) ).
tcf(c_23093,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_22675]) ).
tcf(c_23094,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_22675]) ).
tcf(c_23096,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_22675]) ).
tcf(c_23097,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_22675]) ).
tcf(c_23098,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_22675]) ).
tcf(c_23110,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_22675]) ).
tcf(c_23115,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_22675]) ).
tcf(c_23116,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_22675]) ).
tcf(c_23117,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_22675]) ).
tcf(c_23118,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_22675]) ).
tcf(c_23119,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_22675]) ).
tcf(c_23128,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23058,c_65,c_64]) ).
tcf(c_23299,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8171,c_87]) ).
tcf(c_23300,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK1 = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8171,c_13488]) ).
tcf(c_23301,plain,
( ( sK1 = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8171,c_12807]) ).
tcf(c_23302,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK1 = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8171,c_4623]) ).
tcf(c_23303,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(sK1,empty_set)) = sK23(sK1,empty_set) )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8171,c_4763]) ).
tcf(c_23316,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_23299,c_4030]) ).
tcf(c_23317,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23316,c_987,c_3611]) ).
tcf(c_23369,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14069]) ).
tcf(c_23370,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14069]) ).
tcf(c_23371,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14069]) ).
tcf(c_23372,plain,
relation_inverse(relation_dom(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14069]) ).
tcf(c_23373,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14069]) ).
tcf(c_23374,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14069]) ).
tcf(c_23375,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14069]) ).
tcf(c_23376,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14069]) ).
tcf(c_23377,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14069]) ).
tcf(c_23378,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14069]) ).
tcf(c_23404,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14070]) ).
tcf(c_23405,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14070]) ).
tcf(c_23406,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14070]) ).
tcf(c_23407,plain,
relation_inverse(relation_dom(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14070]) ).
tcf(c_23408,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14070]) ).
tcf(c_23409,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14070]) ).
tcf(c_23410,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14070]) ).
tcf(c_23411,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14070]) ).
tcf(c_23412,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14070]) ).
tcf(c_23413,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14070]) ).
tcf(c_23518,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14153]) ).
tcf(c_23519,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14153]) ).
tcf(c_23520,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14153]) ).
tcf(c_23521,plain,
relation_inverse(relation_rng(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14153]) ).
tcf(c_23522,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14153]) ).
tcf(c_23523,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14153]) ).
tcf(c_23524,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14153]) ).
tcf(c_23525,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14153]) ).
tcf(c_23526,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14153]) ).
tcf(c_23527,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14153]) ).
tcf(c_23536,plain,
( ( relation_inverse(relation_rng(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_23522,c_4030]) ).
tcf(c_23555,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14154]) ).
tcf(c_23556,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14154]) ).
tcf(c_23557,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14154]) ).
tcf(c_23558,plain,
relation_inverse(relation_rng(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14154]) ).
tcf(c_23559,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14154]) ).
tcf(c_23560,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14154]) ).
tcf(c_23561,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14154]) ).
tcf(c_23562,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14154]) ).
tcf(c_23563,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14154]) ).
tcf(c_23564,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14154]) ).
tcf(c_23643,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_18437]) ).
tcf(c_23646,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_18437]) ).
tcf(c_23647,plain,
! [X0: $i] :
( in(sK15(sK2,X0),relation_dom(sK2))
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_107,c_18437]) ).
tcf(c_23648,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| in(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_18437]) ).
tcf(c_23649,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| in(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_18437]) ).
tcf(c_23650,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| in(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_18437]) ).
tcf(c_23651,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_18437]) ).
tcf(c_23652,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15114,c_18437]) ).
tcf(c_23653,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_18437]) ).
tcf(c_23654,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_18437]) ).
tcf(c_23655,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_18437]) ).
tcf(c_23656,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_18437]) ).
tcf(c_23657,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_18437]) ).
tcf(c_23658,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_18437]) ).
tcf(c_23659,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_18437]) ).
tcf(c_23660,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_18437]) ).
tcf(c_23661,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_18437]) ).
tcf(c_23662,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_18437]) ).
tcf(c_23663,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_18437]) ).
tcf(c_23664,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_18437]) ).
tcf(c_23665,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_18437]) ).
tcf(c_23666,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_18437]) ).
tcf(c_23667,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_18437]) ).
tcf(c_23670,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| in(sK21(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_18437]) ).
tcf(c_23671,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_18437]) ).
tcf(c_23673,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23667,c_61]) ).
tcf(c_23677,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23663,c_61]) ).
tcf(c_23681,plain,
! [X0: $i] :
( in(sK15(sK2,X0),relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23647,c_61]) ).
tcf(c_23689,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23659,c_61]) ).
tcf(c_23694,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23657,c_61]) ).
tcf(c_23699,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23655,c_61]) ).
tcf(c_23704,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23653,c_61]) ).
tcf(c_23709,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23646,c_61]) ).
tcf(c_23714,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23643,c_61]) ).
tcf(c_23719,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23671,c_61]) ).
tcf(c_23724,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| in(sK21(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23670,c_61]) ).
tcf(c_23729,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23665,c_61]) ).
tcf(c_23735,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23658,c_61]) ).
tcf(c_23740,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23654,c_61]) ).
tcf(c_23745,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23666,c_61]) ).
tcf(c_23750,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23662,c_61]) ).
tcf(c_23755,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23651,c_61]) ).
tcf(c_23761,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| in(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23650,c_61]) ).
tcf(c_23767,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| in(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23649,c_61]) ).
tcf(c_23773,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| in(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23648,c_61]) ).
tcf(c_23791,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK21(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_70]) ).
tcf(c_23792,plain,
( element(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_69]) ).
tcf(c_23793,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_67]) ).
tcf(c_23794,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_22656]) ).
tcf(c_23796,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_12701]) ).
tcf(c_23798,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_10144]) ).
tcf(c_23799,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_8393]) ).
tcf(c_23800,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK15(sK1,sK21(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_4468]) ).
tcf(c_23831,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK22(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_23677,c_70]) ).
tcf(c_23832,plain,
( element(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_69]) ).
tcf(c_23833,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_67]) ).
tcf(c_23834,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_22656]) ).
tcf(c_23836,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_12701]) ).
tcf(c_23838,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_10144]) ).
tcf(c_23839,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_8393]) ).
tcf(c_23840,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK15(sK1,sK22(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_4468]) ).
tcf(c_23898,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2))
| ~ in(relation_dom(sK2),sK15(sK2,X0)) ),
inference(superposition,[status(thm)],[c_23681,c_70]) ).
tcf(c_23899,plain,
! [X0: $i] :
( element(sK15(sK2,X0),relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_69]) ).
tcf(c_23900,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_67]) ).
tcf(c_23901,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_22656]) ).
tcf(c_23902,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_15043]) ).
tcf(c_23903,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK15(sK2,X0))) = sK15(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_12701]) ).
tcf(c_23904,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_10124]) ).
tcf(c_23905,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK15(sK2,X0))) = sK15(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_10144]) ).
tcf(c_23906,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_8393]) ).
tcf(c_23907,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK15(sK2,X0)) = sK15(sK1,sK15(sK2,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_4468]) ).
tcf(c_23956,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_70]) ).
tcf(c_23957,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_69]) ).
tcf(c_23958,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_67]) ).
tcf(c_23959,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_22656]) ).
tcf(c_23961,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_12701]) ).
tcf(c_23963,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_10144]) ).
tcf(c_23964,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_8393]) ).
tcf(c_23965,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_4468]) ).
tcf(c_24085,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_70]) ).
tcf(c_24086,plain,
( element(sK23(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_69]) ).
tcf(c_24087,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_67]) ).
tcf(c_24090,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_12701]) ).
tcf(c_24092,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_10144]) ).
tcf(c_24093,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_8393]) ).
tcf(c_24094,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_4468]) ).
tcf(c_24131,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_23699,c_70]) ).
tcf(c_24132,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_69]) ).
tcf(c_24133,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_67]) ).
tcf(c_24134,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_22656]) ).
tcf(c_24136,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_12701]) ).
tcf(c_24138,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_10144]) ).
tcf(c_24139,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_8393]) ).
tcf(c_24140,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_4468]) ).
tcf(c_24208,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_23704,c_70]) ).
tcf(c_24209,plain,
( element(sK23(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_69]) ).
tcf(c_24210,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_67]) ).
tcf(c_24213,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_12701]) ).
tcf(c_24215,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_10144]) ).
tcf(c_24216,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_8393]) ).
tcf(c_24217,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_4468]) ).
tcf(c_24254,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8174,c_87]) ).
tcf(c_24255,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8174,c_13488]) ).
tcf(c_24256,plain,
( ( sK1 = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8174,c_12807]) ).
tcf(c_24257,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8174,c_4623]) ).
tcf(c_24258,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(empty_set,sK1)) = sK23(empty_set,sK1) )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8174,c_4763]) ).
tcf(c_24271,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_24254,c_4030]) ).
tcf(c_24272,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24271,c_987,c_3611]) ).
tcf(c_24297,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14155]) ).
tcf(c_24298,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14155]) ).
tcf(c_24299,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14155]) ).
tcf(c_24300,plain,
relation_inverse(relation_rng(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14155]) ).
tcf(c_24301,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14155]) ).
tcf(c_24302,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14155]) ).
tcf(c_24303,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14155]) ).
tcf(c_24304,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14155]) ).
tcf(c_24305,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14155]) ).
tcf(c_24306,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14155]) ).
tcf(c_24359,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14233]) ).
tcf(c_24360,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14233]) ).
tcf(c_24361,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14233]) ).
tcf(c_24362,plain,
relation_inverse(relation_inverse(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14233]) ).
tcf(c_24363,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14233]) ).
tcf(c_24364,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14233]) ).
tcf(c_24365,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14233]) ).
tcf(c_24366,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14233]) ).
tcf(c_24367,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14233]) ).
tcf(c_24368,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14233]) ).
tcf(c_24377,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_24363,c_4030]) ).
tcf(c_24396,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14234]) ).
tcf(c_24397,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14234]) ).
tcf(c_24398,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14234]) ).
tcf(c_24399,plain,
relation_inverse(relation_inverse(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14234]) ).
tcf(c_24400,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14234]) ).
tcf(c_24401,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14234]) ).
tcf(c_24402,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14234]) ).
tcf(c_24403,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14234]) ).
tcf(c_24404,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14234]) ).
tcf(c_24405,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14234]) ).
tcf(c_24510,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14235]) ).
tcf(c_24511,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14235]) ).
tcf(c_24512,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14235]) ).
tcf(c_24513,plain,
relation_inverse(relation_inverse(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14235]) ).
tcf(c_24514,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14235]) ).
tcf(c_24515,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14235]) ).
tcf(c_24516,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14235]) ).
tcf(c_24517,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14235]) ).
tcf(c_24518,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14235]) ).
tcf(c_24519,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14235]) ).
tcf(c_24567,plain,
! [X0: $i] :
( in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,sK13(sK2,X0)) ),
inference(superposition,[status(thm)],[c_23709,c_70]) ).
tcf(c_24568,plain,
! [X0: $i] :
( element(sK13(sK2,X0),X0)
| in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_69]) ).
tcf(c_24569,plain,
! [X0: $i] :
( in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_67]) ).
tcf(c_24570,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_22675]) ).
tcf(c_24571,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_15040]) ).
tcf(c_24572,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK13(sK2,relation_dom(sK1))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12284]) ).
tcf(c_24573,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10726]) ).
tcf(c_24574,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_5348]) ).
tcf(c_24575,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4619]) ).
tcf(c_24576,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4406]) ).
tcf(c_24577,plain,
( in(sK14(sK2,empty_set),relation_dom(sK2))
| ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8115]) ).
tcf(c_24578,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_22656]) ).
tcf(c_24579,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_15043]) ).
tcf(c_24580,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12701]) ).
tcf(c_24581,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10124]) ).
tcf(c_24582,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10144]) ).
tcf(c_24583,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8393]) ).
tcf(c_24584,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK2,relation_dom(sK2))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4468]) ).
tcf(c_24585,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK2,sK19(X0)),X0)
| in(sK14(sK2,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4215]) ).
tcf(c_24586,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(powerset(X0))),X0)
| in(sK14(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4216]) ).
tcf(c_24587,plain,
! [X0: $i] :
( in(sK14(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4201]) ).
tcf(c_24588,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK14(sK2,X0)) ),
inference(superposition,[status(thm)],[c_23709,c_70]) ).
tcf(c_24589,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| element(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_69]) ).
tcf(c_24590,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_67]) ).
tcf(c_24592,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_15043]) ).
tcf(c_24593,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12701]) ).
tcf(c_24594,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10124]) ).
tcf(c_24595,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10144]) ).
tcf(c_24596,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8393]) ).
tcf(c_24597,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK14(sK2,X0)) = sK15(sK1,sK14(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4468]) ).
tcf(c_24795,plain,
! [X0: $i] :
( in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,sK5(sK2,X0)) ),
inference(superposition,[status(thm)],[c_23714,c_70]) ).
tcf(c_24796,plain,
! [X0: $i] :
( element(sK5(sK2,X0),X0)
| in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_69]) ).
tcf(c_24797,plain,
! [X0: $i] :
( in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_67]) ).
tcf(c_24798,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_22675]) ).
tcf(c_24800,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK5(sK2,relation_dom(sK1))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_12284]) ).
tcf(c_24803,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4619]) ).
tcf(c_24804,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4406]) ).
tcf(c_24805,plain,
( in(sK5(sK2,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_8115]) ).
tcf(c_24813,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK2,sK19(X0)),X0)
| in(sK5(sK2,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4215]) ).
tcf(c_24814,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(powerset(X0))),X0)
| in(sK5(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4216]) ).
tcf(c_24815,plain,
! [X0: $i] :
( in(sK5(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4201]) ).
tcf(c_24816,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK5(sK2,X0)) ),
inference(superposition,[status(thm)],[c_23714,c_70]) ).
tcf(c_24817,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| element(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_69]) ).
tcf(c_24818,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_67]) ).
tcf(c_24820,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_15043]) ).
tcf(c_24821,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_12701]) ).
tcf(c_24822,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_10124]) ).
tcf(c_24823,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_10144]) ).
tcf(c_24824,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_8393]) ).
tcf(c_24825,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK5(sK2,X0)) = sK15(sK1,sK5(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4468]) ).
tcf(c_25018,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK22(sK2,sK2)) ),
inference(superposition,[status(thm)],[c_23719,c_70]) ).
tcf(c_25019,plain,
( element(sK22(sK2,sK2),relation_rng(sK2))
| in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23719,c_69]) ).
tcf(c_25020,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23719,c_67]) ).
tcf(c_25041,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK21(sK2,sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_70]) ).
tcf(c_25042,plain,
( element(sK21(sK2,sK2),relation_rng(sK2))
| in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_69]) ).
tcf(c_25043,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_67]) ).
tcf(c_25066,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_70]) ).
tcf(c_25067,plain,
( element(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_69]) ).
tcf(c_25068,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_67]) ).
tcf(c_25070,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_15043]) ).
tcf(c_25071,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_12701]) ).
tcf(c_25072,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_10124]) ).
tcf(c_25073,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_10144]) ).
tcf(c_25074,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_8393]) ).
tcf(c_25075,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_4468]) ).
tcf(c_25147,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_23740,c_70]) ).
tcf(c_25148,plain,
( element(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_69]) ).
tcf(c_25149,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_67]) ).
tcf(c_25151,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_15043]) ).
tcf(c_25152,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_12701]) ).
tcf(c_25153,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_10124]) ).
tcf(c_25154,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_10144]) ).
tcf(c_25155,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_8393]) ).
tcf(c_25156,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_4468]) ).
tcf(c_25203,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),relation_inverse(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8177,c_87]) ).
tcf(c_25204,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1)
| ( relation_inverse(sK1) = empty_set )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8177,c_13488]) ).
tcf(c_25205,plain,
( ( relation_inverse(sK1) = empty_set )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8177,c_12807]) ).
tcf(c_25206,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1)
| ( relation_inverse(sK1) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8177,c_4623]) ).
tcf(c_25207,plain,
( ( relation_inverse(sK1) = empty_set )
| ( sK15(sK1,sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8177,c_4763]) ).
tcf(c_25220,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),relation_inverse(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_25203,c_4030]) ).
tcf(c_25221,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),relation_inverse(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25220,c_987,c_3611]) ).
tcf(c_25246,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14778]) ).
tcf(c_25247,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14778]) ).
tcf(c_25248,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14778]) ).
tcf(c_25249,plain,
sK20(powerset(relation_dom(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14778]) ).
tcf(c_25250,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14778]) ).
tcf(c_25251,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14778]) ).
tcf(c_25252,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14778]) ).
tcf(c_25253,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14778]) ).
tcf(c_25254,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14778]) ).
tcf(c_25255,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14778]) ).
tcf(c_25264,plain,
( ( sK20(powerset(relation_dom(sK2))) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_25250,c_4030]) ).
tcf(c_25310,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14779]) ).
tcf(c_25311,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14779]) ).
tcf(c_25312,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14779]) ).
tcf(c_25313,plain,
sK20(powerset(relation_rng(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14779]) ).
tcf(c_25314,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14779]) ).
tcf(c_25315,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14779]) ).
tcf(c_25316,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14779]) ).
tcf(c_25317,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14779]) ).
tcf(c_25318,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14779]) ).
tcf(c_25319,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14779]) ).
tcf(c_25345,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14780]) ).
tcf(c_25346,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14780]) ).
tcf(c_25347,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14780]) ).
tcf(c_25348,plain,
sK20(powerset(relation_inverse(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14780]) ).
tcf(c_25349,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_14780]) ).
tcf(c_25350,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_14780]) ).
tcf(c_25351,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_14780]) ).
tcf(c_25352,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_14780]) ).
tcf(c_25353,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_14780]) ).
tcf(c_25354,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14780]) ).
tcf(c_25360,plain,
( ( sK20(powerset(sK2)) = empty_set )
| ~ empty(sK1) ),
inference(light_normalisation,[status(thm)],[c_25351,c_3624]) ).
tcf(c_25365,plain,
( ( sK20(powerset(sK1)) = empty_set )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_25349,c_3625]) ).
tcf(c_25430,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK23(sK2,X0),sK24(sK2,X0))) ),
inference(superposition,[status(thm)],[c_23755,c_70]) ).
tcf(c_25431,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| element(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_69]) ).
tcf(c_25432,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| ( X0 = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_67]) ).
tcf(c_25433,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| in(sK24(sK2,X0),relation_rng(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_106]) ).
tcf(c_25434,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| in(sK23(sK2,X0),relation_dom(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_78]) ).
tcf(c_25435,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| ( X0 = sK2 )
| ( apply(X0,sK23(sK2,X0)) = sK24(sK2,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_197]) ).
tcf(c_25436,plain,
! [X0: $i] :
( in(sK23(sK2,relation_inverse(X0)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(X0)),sK23(sK2,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_23755,c_297]) ).
tcf(c_25437,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| ( X0 = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),sK2) ),
inference(superposition,[status(thm)],[c_23755,c_129]) ).
tcf(c_25438,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_22675]) ).
tcf(c_25439,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_15040]) ).
tcf(c_25440,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_12284]) ).
tcf(c_25441,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_10726]) ).
tcf(c_25442,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_5348]) ).
tcf(c_25443,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_4619]) ).
tcf(c_25444,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_4406]) ).
tcf(c_25447,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_3774]) ).
tcf(c_25448,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_4259]) ).
tcf(c_25449,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_4237]) ).
tcf(c_25450,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_3784]) ).
tcf(c_25451,plain,
( in(sK23(sK2,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK1)),sK23(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_3719]) ).
tcf(c_25452,plain,
( in(sK23(sK2,empty_set),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_8115]) ).
tcf(c_25453,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_22656]) ).
tcf(c_25454,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_15043]) ).
tcf(c_25455,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_12701]) ).
tcf(c_25456,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_10124]) ).
tcf(c_25457,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_10144]) ).
tcf(c_25458,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_8393]) ).
tcf(c_25459,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_4468]) ).
tcf(c_25460,plain,
! [X0: $i] :
( empty(X0)
| in(sK23(sK2,sK19(X0)),relation_dom(sK2))
| element(ordered_pair(sK23(sK2,sK19(X0)),sK24(sK2,sK19(X0))),X0)
| ( sK19(X0) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_23755,c_4215]) ).
tcf(c_25461,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(powerset(X0))),relation_dom(sK2))
| element(ordered_pair(sK23(sK2,sK20(powerset(X0))),sK24(sK2,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23755,c_4216]) ).
tcf(c_25462,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23755,c_4201]) ).
tcf(c_25463,plain,
( in(sK23(sK2,empty_set),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25452,c_135]) ).
tcf(c_25541,plain,
! [X0: $i] :
( in(sK23(sK2,X0),relation_dom(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK23(sK2,X0),sK24(sK2,X0)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25437,c_61]) ).
tcf(c_25553,plain,
( in(sK23(sK2,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK1)),sK23(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25451,c_3611]) ).
tcf(c_25749,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK23(X0,sK2),sK24(X0,sK2))) ),
inference(superposition,[status(thm)],[c_23761,c_70]) ).
tcf(c_25750,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| element(ordered_pair(sK23(X0,sK2),sK24(X0,sK2)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_69]) ).
tcf(c_25751,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| ( X0 = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_67]) ).
tcf(c_25752,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| in(sK24(X0,sK2),relation_rng(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_106]) ).
tcf(c_25753,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| in(sK23(X0,sK2),relation_dom(X0))
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_78]) ).
tcf(c_25754,plain,
! [X0: $i] :
( in(sK23(X0,sK2),relation_dom(sK2))
| ( X0 = sK2 )
| ( apply(X0,sK23(X0,sK2)) = sK24(X0,sK2) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_197]) ).
tcf(c_25755,plain,
! [X0: $i] :
( in(sK23(relation_inverse(X0),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(X0),sK2),sK23(relation_inverse(X0),sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_23761,c_297]) ).
tcf(c_25757,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_22675]) ).
tcf(c_25758,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_15040]) ).
tcf(c_25759,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_12284]) ).
tcf(c_25760,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_10726]) ).
tcf(c_25761,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_5348]) ).
tcf(c_25762,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_4619]) ).
tcf(c_25763,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_4406]) ).
tcf(c_25766,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_3774]) ).
tcf(c_25767,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_4259]) ).
tcf(c_25768,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_4237]) ).
tcf(c_25769,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_3784]) ).
tcf(c_25770,plain,
( in(sK23(relation_inverse(sK1),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK2),sK23(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_3719]) ).
tcf(c_25771,plain,
( in(sK23(empty_set,sK2),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_8115]) ).
tcf(c_25772,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_22656]) ).
tcf(c_25773,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_15043]) ).
tcf(c_25774,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_12701]) ).
tcf(c_25775,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_10124]) ).
tcf(c_25776,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_10144]) ).
tcf(c_25777,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_8393]) ).
tcf(c_25778,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_4468]) ).
tcf(c_25779,plain,
! [X0: $i] :
( empty(X0)
| in(sK23(sK19(X0),sK2),relation_dom(sK2))
| element(ordered_pair(sK23(sK19(X0),sK2),sK24(sK19(X0),sK2)),X0)
| ( sK19(X0) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_23761,c_4215]) ).
tcf(c_25780,plain,
! [X0: $i] :
( in(sK23(sK20(powerset(X0)),sK2),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(powerset(X0)),sK2),sK24(sK20(powerset(X0)),sK2)),X0)
| ( sK20(powerset(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23761,c_4216]) ).
tcf(c_25781,plain,
! [X0: $i] :
( in(sK23(sK20(powerset(X0)),sK2),relation_dom(sK2))
| ( sK20(powerset(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23761,c_4201]) ).
tcf(c_25782,plain,
( in(sK23(empty_set,sK2),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25771,c_135]) ).
tcf(c_25866,plain,
( in(sK23(relation_inverse(sK1),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK1),sK2),sK23(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25770,c_3611]) ).
tcf(c_26012,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK22(X0,sK2),sK21(X0,sK2))) ),
inference(superposition,[status(thm)],[c_23767,c_70]) ).
tcf(c_26013,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| element(ordered_pair(sK22(X0,sK2),sK21(X0,sK2)),X0)
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_69]) ).
tcf(c_26014,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_67]) ).
tcf(c_26015,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| in(sK21(X0,sK2),relation_rng(X0))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_106]) ).
tcf(c_26016,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| in(sK22(X0,sK2),relation_dom(X0))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_78]) ).
tcf(c_26017,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| ( relation_inverse(X0) = sK2 )
| ( apply(X0,sK22(X0,sK2)) = sK21(X0,sK2) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_197]) ).
tcf(c_26018,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(sK2)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(X0,sK2),sK22(X0,sK2)),sK2) ),
inference(superposition,[status(thm)],[c_23767,c_124]) ).
tcf(c_26019,plain,
! [X0: $i] :
( in(sK21(relation_inverse(X0),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(X0),sK2),sK22(relation_inverse(X0),sK2)),X0)
| ( relation_inverse(relation_inverse(X0)) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_23767,c_297]) ).
tcf(c_26020,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_22675]) ).
tcf(c_26021,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_15040]) ).
tcf(c_26022,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( sK15(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_12284]) ).
tcf(c_26023,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_10726]) ).
tcf(c_26024,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_5348]) ).
tcf(c_26025,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_4619]) ).
tcf(c_26026,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_4406]) ).
tcf(c_26027,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_18437]) ).
tcf(c_26029,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_3774]) ).
tcf(c_26030,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_4259]) ).
tcf(c_26031,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_4237]) ).
tcf(c_26032,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_3784]) ).
tcf(c_26033,plain,
( in(sK21(relation_inverse(sK1),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( relation_inverse(relation_inverse(sK1)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_3719]) ).
tcf(c_26034,plain,
( in(sK21(empty_set,sK2),relation_dom(sK2))
| ( relation_inverse(empty_set) = sK2 )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_8115]) ).
tcf(c_26035,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_22656]) ).
tcf(c_26036,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_15043]) ).
tcf(c_26037,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_12701]) ).
tcf(c_26038,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_10124]) ).
tcf(c_26039,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_10144]) ).
tcf(c_26040,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_8393]) ).
tcf(c_26041,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_4468]) ).
tcf(c_26042,plain,
! [X0: $i] :
( empty(X0)
| in(sK21(sK19(X0),sK2),relation_dom(sK2))
| element(ordered_pair(sK22(sK19(X0),sK2),sK21(sK19(X0),sK2)),X0)
| ( relation_inverse(sK19(X0)) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_23767,c_4215]) ).
tcf(c_26043,plain,
! [X0: $i] :
( in(sK21(sK20(powerset(X0)),sK2),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(powerset(X0)),sK2),sK21(sK20(powerset(X0)),sK2)),X0)
| ( relation_inverse(sK20(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23767,c_4216]) ).
tcf(c_26044,plain,
! [X0: $i] :
( in(sK21(sK20(powerset(X0)),sK2),relation_dom(sK2))
| ( relation_inverse(sK20(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23767,c_4201]) ).
tcf(c_26045,plain,
( in(sK21(empty_set,sK2),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_26034,c_8232]) ).
tcf(c_26046,plain,
( in(sK21(empty_set,sK2),relation_dom(sK2))
| ( sK2 = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26045,c_135]) ).
tcf(c_26063,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26027,c_61]) ).
tcf(c_26129,plain,
! [X0: $i] :
( in(sK21(X0,sK2),relation_dom(sK2))
| ( relation_inverse(X0) = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(ordered_pair(sK21(X0,sK2),sK22(X0,sK2)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26018,c_61]) ).
tcf(c_26141,plain,
( in(sK21(relation_inverse(sK1),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_26033,c_3625]) ).
tcf(c_26142,plain,
( in(sK21(relation_inverse(sK1),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK1),sK2),sK22(relation_inverse(sK1),sK2)),sK1)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26141,c_3611]) ).
tcf(c_26290,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK21(sK2,sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_70]) ).
tcf(c_26291,plain,
( element(sK21(sK2,sK2),relation_dom(sK2))
| in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_69]) ).
tcf(c_26292,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_67]) ).
tcf(c_26294,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_15043]) ).
tcf(c_26295,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK2,sK2))) = sK21(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_12701]) ).
tcf(c_26296,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_10124]) ).
tcf(c_26297,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK2,sK2))) = sK21(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_10144]) ).
tcf(c_26298,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_8393]) ).
tcf(c_26299,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK2,sK2)) = sK15(sK1,sK21(sK2,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_4468]) ).
tcf(c_26373,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,ordered_pair(sK21(sK2,X0),sK22(sK2,X0))) ),
inference(superposition,[status(thm)],[c_23773,c_70]) ).
tcf(c_26374,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| element(ordered_pair(sK21(sK2,X0),sK22(sK2,X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_69]) ).
tcf(c_26375,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| ( relation_inverse(sK2) = X0 )
| ~ empty(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_67]) ).
tcf(c_26376,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| in(sK22(sK2,X0),relation_rng(X0))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_106]) ).
tcf(c_26377,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| in(sK21(sK2,X0),relation_dom(X0))
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_78]) ).
tcf(c_26378,plain,
! [X0: $i] :
( in(sK22(sK2,X0),relation_dom(sK2))
| ( relation_inverse(sK2) = X0 )
| ( apply(X0,sK21(sK2,X0)) = sK22(sK2,X0) )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_197]) ).
tcf(c_26379,plain,
! [X0: $i] :
( in(sK22(sK2,relation_inverse(X0)),relation_dom(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(X0)),sK21(sK2,relation_inverse(X0))),X0)
| ( relation_inverse(X0) = relation_inverse(sK2) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(X0)) ),
inference(superposition,[status(thm)],[c_23773,c_297]) ).
tcf(c_26380,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_22675]) ).
tcf(c_26381,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_15040]) ).
tcf(c_26382,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_12284]) ).
tcf(c_26383,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_10726]) ).
tcf(c_26384,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_5348]) ).
tcf(c_26385,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_4619]) ).
tcf(c_26386,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_4406]) ).
tcf(c_26389,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_3774]) ).
tcf(c_26390,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_4259]) ).
tcf(c_26391,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_4237]) ).
tcf(c_26392,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ relation(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_3784]) ).
tcf(c_26393,plain,
( in(sK22(sK2,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK1)),sK21(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_3719]) ).
tcf(c_26394,plain,
( in(sK22(sK2,empty_set),relation_dom(sK2))
| ( relation_inverse(sK2) = empty_set )
| ~ relation(empty_set)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_8115]) ).
tcf(c_26395,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_22656]) ).
tcf(c_26396,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_15043]) ).
tcf(c_26397,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_12701]) ).
tcf(c_26398,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_10124]) ).
tcf(c_26399,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_10144]) ).
tcf(c_26400,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_8393]) ).
tcf(c_26401,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_4468]) ).
tcf(c_26402,plain,
! [X0: $i] :
( empty(X0)
| in(sK22(sK2,sK19(X0)),relation_dom(sK2))
| element(ordered_pair(sK21(sK2,sK19(X0)),sK22(sK2,sK19(X0))),X0)
| ( sK19(X0) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK19(X0)) ),
inference(superposition,[status(thm)],[c_23773,c_4215]) ).
tcf(c_26403,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(powerset(X0))),relation_dom(sK2))
| element(ordered_pair(sK21(sK2,sK20(powerset(X0))),sK22(sK2,sK20(powerset(X0)))),X0)
| ( sK20(powerset(X0)) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23773,c_4216]) ).
tcf(c_26404,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_23773,c_4201]) ).
tcf(c_26405,plain,
( in(sK22(sK2,empty_set),relation_dom(sK2))
| ( relation_inverse(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26394,c_135]) ).
tcf(c_26489,plain,
( in(sK22(sK2,relation_inverse(sK1)),relation_dom(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK1)),sK21(sK2,relation_inverse(sK1))),sK1)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26393,c_3611]) ).
tcf(c_26641,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_8180,c_8232]) ).
tcf(c_26652,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_26641,c_87]) ).
tcf(c_26653,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_26641,c_13488]) ).
tcf(c_26654,plain,
( ( sK1 = empty_set )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_26641,c_12807]) ).
tcf(c_26655,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_26641,c_4623]) ).
tcf(c_26656,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK22(empty_set,sK1)) = sK21(empty_set,sK1) )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_26641,c_4763]) ).
tcf(c_26669,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_26652,c_4030]) ).
tcf(c_26670,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26669,c_987,c_3611]) ).
tcf(c_26722,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23904,c_9882,c_23904]) ).
tcf(c_26729,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK2),X0),X0)
| ( relation_dom(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_26722]) ).
tcf(c_26730,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_26722]) ).
tcf(c_26731,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ function(relation_rng(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_26722]) ).
tcf(c_26732,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK2),X0),X0)
| ( relation_rng(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_26722]) ).
tcf(c_26733,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_rng(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_26722]) ).
tcf(c_26734,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0)
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_26722]) ).
tcf(c_26735,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK2)),sK21(X0,relation_rng(sK2))),X0)
| ( relation_inverse(X0) = relation_rng(sK2) )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_26722]) ).
tcf(c_26736,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_26722]) ).
tcf(c_26737,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(sK1)
| ~ relation(X0)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_26722]) ).
tcf(c_26742,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10732,c_26722]) ).
tcf(c_26745,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK2))) = sK5(sK1,relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5141,c_26722]) ).
tcf(c_26749,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_10736,c_26722]) ).
tcf(c_26751,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = sK14(sK1,relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_5563,c_26722]) ).
tcf(c_26754,plain,
( in(sK23(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_26722]) ).
tcf(c_26755,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK2),sK1)) = sK23(relation_rng(sK2),sK1) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_26722]) ).
tcf(c_26756,plain,
( in(sK24(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_26722]) ).
tcf(c_26757,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_26722]) ).
tcf(c_26758,plain,
( in(sK23(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_26722]) ).
tcf(c_26759,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK2))) = sK23(sK1,relation_rng(sK2)) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_26722]) ).
tcf(c_26760,plain,
( in(sK24(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_26722]) ).
tcf(c_26761,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_26722]) ).
tcf(c_26762,plain,
( in(sK21(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_26722]) ).
tcf(c_26763,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK2),sK1)) = sK21(relation_rng(sK2),sK1) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_26722]) ).
tcf(c_26764,plain,
( in(sK22(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_26722]) ).
tcf(c_26765,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_26722]) ).
tcf(c_26766,plain,
( in(sK22(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_26722]) ).
tcf(c_26767,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK2))) = sK22(sK1,relation_rng(sK2)) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_26722]) ).
tcf(c_26768,plain,
( in(sK21(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(sK1)
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_26722]) ).
tcf(c_26771,plain,
( in(sK23(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_26722]) ).
tcf(c_26772,plain,
( in(sK24(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_26722]) ).
tcf(c_26776,plain,
! [X0: $i] :
( ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_26722]) ).
tcf(c_26781,plain,
( in(sK22(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_26722]) ).
tcf(c_26782,plain,
( in(sK21(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_26722]) ).
tcf(c_26783,plain,
( in(sK21(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_26722]) ).
tcf(c_26784,plain,
( in(sK22(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_26722]) ).
tcf(c_26785,plain,
( in(sK23(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_26722]) ).
tcf(c_26786,plain,
( in(sK24(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_26722]) ).
tcf(c_26793,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_26722]) ).
tcf(c_26795,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_26722]) ).
tcf(c_26798,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_26722]) ).
tcf(c_26799,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK1)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_26722]) ).
tcf(c_27184,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23793,c_4128,c_13843]) ).
tcf(c_27192,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23794,c_22673,c_27184]) ).
tcf(c_27200,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ empty(relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_23799,c_13837]) ).
tcf(c_27208,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_dom(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23833,c_4128,c_9913]) ).
tcf(c_27216,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23834,c_22673,c_27208]) ).
tcf(c_27224,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ empty(relation_dom(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_23839,c_4036,c_27208]) ).
tcf(c_27242,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),empty_set),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8706,c_87]) ).
tcf(c_27243,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = sK15(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8706,c_4863]) ).
tcf(c_27244,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(relation_dom(sK2),empty_set)
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8706,c_6246]) ).
tcf(c_27247,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = apply(relation_inverse(sK1),empty_set) )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8706,c_4791]) ).
tcf(c_27248,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8706,c_8695]) ).
tcf(c_27281,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(X0)))) = relation_dom(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3626]) ).
tcf(c_27282,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(X0)))) = relation_dom(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3626]) ).
tcf(c_27283,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(X0)))) = relation_dom(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3626]) ).
tcf(c_27284,plain,
relation_inverse(relation_inverse(relation_dom(empty_set))) = relation_dom(empty_set),
inference(superposition,[status(thm)],[c_136,c_3626]) ).
tcf(c_27285,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK1)))) = relation_dom(relation_inverse(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3626]) ).
tcf(c_27286,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK1)))) = relation_dom(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3626]) ).
tcf(c_27287,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK2)))) = relation_dom(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3626]) ).
tcf(c_27288,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK2)))) = relation_dom(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3626]) ).
tcf(c_27289,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK2)))) = relation_dom(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3626]) ).
tcf(c_27290,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0))))) = relation_dom(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3626]) ).
tcf(c_27299,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ empty(sK2) ),
inference(light_normalisation,[status(thm)],[c_27285,c_4030]) ).
tcf(c_27318,plain,
relation_inverse(relation_inverse(relation_inverse(sK2))) = relation_inverse(sK2),
inference(superposition,[status(thm)],[c_61,c_3630]) ).
tcf(c_27320,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(X0)))) = relation_inverse(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_3630]) ).
tcf(c_27321,plain,
relation_inverse(relation_inverse(relation_inverse(sK9))) = relation_inverse(sK9),
inference(superposition,[status(thm)],[c_83,c_3630]) ).
tcf(c_27322,plain,
relation_inverse(relation_inverse(relation_inverse(sK10))) = relation_inverse(sK10),
inference(superposition,[status(thm)],[c_91,c_3630]) ).
tcf(c_27324,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_inverse(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_3630]) ).
tcf(c_27325,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_inverse(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_3630]) ).
tcf(c_27326,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(X0)))) = relation_inverse(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_3630]) ).
tcf(c_27327,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(function_inverse(X0)))) = relation_inverse(function_inverse(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_3630]) ).
tcf(c_27328,plain,
relation_inverse(relation_inverse(relation_inverse(empty_set))) = relation_inverse(empty_set),
inference(superposition,[status(thm)],[c_135,c_3630]) ).
tcf(c_27329,plain,
relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK1)))) = relation_inverse(relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_3611,c_3630]) ).
tcf(c_27330,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK1)))) = relation_inverse(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7609,c_3630]) ).
tcf(c_27331,plain,
relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK12)))) = relation_inverse(relation_inverse(sK12)),
inference(superposition,[status(thm)],[c_3610,c_3630]) ).
tcf(c_27332,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK2)))) = relation_inverse(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9882,c_3630]) ).
tcf(c_27333,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK2)))) = relation_inverse(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9888,c_3630]) ).
tcf(c_27334,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK2)))) = relation_inverse(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4120,c_3630]) ).
tcf(c_27335,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0))))) = relation_inverse(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_3630]) ).
tcf(c_27376,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK1)))) = relation_inverse(relation_inverse(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3631]) ).
tcf(c_27399,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12146]) ).
tcf(c_27400,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12146]) ).
tcf(c_27401,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12146]) ).
tcf(c_27402,plain,
relation_inverse(sK20(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12146]) ).
tcf(c_27403,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_12146]) ).
tcf(c_27404,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK1)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_12146]) ).
tcf(c_27405,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_12146]) ).
tcf(c_27406,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_12146]) ).
tcf(c_27407,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK2)))) = empty_set )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_12146]) ).
tcf(c_27408,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12146]) ).
tcf(c_27478,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23900,c_4128,c_26722]) ).
tcf(c_27485,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK2),X0),X0)
| ( relation_dom(relation_rng(sK2)) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_27478]) ).
tcf(c_27486,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_27478]) ).
tcf(c_27487,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ function(relation_rng(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_27478]) ).
tcf(c_27488,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK2),X0),X0)
| ( relation_rng(relation_rng(sK2)) = X0 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_27478]) ).
tcf(c_27489,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_rng(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_27478]) ).
tcf(c_27490,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0)
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_27478]) ).
tcf(c_27491,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK2)),sK21(X0,relation_rng(sK2))),X0)
| ( relation_inverse(X0) = relation_rng(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_27478]) ).
tcf(c_27492,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_27478]) ).
tcf(c_27493,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_27478]) ).
tcf(c_27494,plain,
( empty(relation_rng(sK2))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_27478]) ).
tcf(c_27495,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15072,c_27478]) ).
tcf(c_27497,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_27478]) ).
tcf(c_27501,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK2))) = sK5(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5141,c_27478]) ).
tcf(c_27502,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15068,c_27478]) ).
tcf(c_27504,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_27478]) ).
tcf(c_27507,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = sK14(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5563,c_27478]) ).
tcf(c_27510,plain,
( in(sK23(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_27478]) ).
tcf(c_27511,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK2),sK1)) = sK23(relation_rng(sK2),sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_27478]) ).
tcf(c_27512,plain,
( in(sK24(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_27478]) ).
tcf(c_27513,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_27478]) ).
tcf(c_27514,plain,
( in(sK23(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_27478]) ).
tcf(c_27515,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK2))) = sK23(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_27478]) ).
tcf(c_27516,plain,
( in(sK24(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_27478]) ).
tcf(c_27517,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_27478]) ).
tcf(c_27518,plain,
( in(sK21(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_27478]) ).
tcf(c_27519,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK2),sK1)) = sK21(relation_rng(sK2),sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_27478]) ).
tcf(c_27520,plain,
( in(sK22(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_27478]) ).
tcf(c_27521,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_27478]) ).
tcf(c_27522,plain,
( in(sK22(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_27478]) ).
tcf(c_27523,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK2))) = sK22(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_27478]) ).
tcf(c_27524,plain,
( in(sK21(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_27478]) ).
tcf(c_27525,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8158,c_27478]) ).
tcf(c_27527,plain,
( in(sK23(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_27478]) ).
tcf(c_27528,plain,
( in(sK24(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_27478]) ).
tcf(c_27532,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_27478]) ).
tcf(c_27537,plain,
( in(sK22(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_27478]) ).
tcf(c_27538,plain,
( in(sK21(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_27478]) ).
tcf(c_27539,plain,
( in(sK21(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_27478]) ).
tcf(c_27540,plain,
( in(sK22(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_27478]) ).
tcf(c_27541,plain,
( in(sK23(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_27478]) ).
tcf(c_27542,plain,
( in(sK24(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_27478]) ).
tcf(c_27545,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18758,c_27478]) ).
tcf(c_27548,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_27478]) ).
tcf(c_27549,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_27478]) ).
tcf(c_27551,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_27478]) ).
tcf(c_27554,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_27478]) ).
tcf(c_27555,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_27478]) ).
tcf(c_28056,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23901,c_22673,c_27478]) ).
tcf(c_28059,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23902,c_3712,c_9882,c_23904]) ).
tcf(c_28066,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK2),X0),X0)
| ( relation_dom(relation_rng(sK2)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_28059]) ).
tcf(c_28067,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_28059]) ).
tcf(c_28068,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ function(relation_rng(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_28059]) ).
tcf(c_28069,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK2),X0),X0)
| ( relation_rng(relation_rng(sK2)) = X0 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_28059]) ).
tcf(c_28070,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_rng(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_28059]) ).
tcf(c_28071,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0)
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_28059]) ).
tcf(c_28072,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK2)),sK21(X0,relation_rng(sK2))),X0)
| ( relation_inverse(X0) = relation_rng(sK2) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_28059]) ).
tcf(c_28073,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_28059]) ).
tcf(c_28074,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_28059]) ).
tcf(c_28075,plain,
( empty(relation_rng(sK2))
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3448,c_28059]) ).
tcf(c_28076,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_28059]) ).
tcf(c_28082,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK2))) = sK5(sK1,relation_rng(sK2)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5141,c_28059]) ).
tcf(c_28083,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_28059]) ).
tcf(c_28088,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = sK14(sK1,relation_rng(sK2)) )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_5563,c_28059]) ).
tcf(c_28092,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK2),sK1)) = sK23(relation_rng(sK2),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_28059]) ).
tcf(c_28094,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_28059]) ).
tcf(c_28096,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK2))) = sK23(sK1,relation_rng(sK2)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_28059]) ).
tcf(c_28098,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_28059]) ).
tcf(c_28100,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK2),sK1)) = sK21(relation_rng(sK2),sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_28059]) ).
tcf(c_28102,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_28059]) ).
tcf(c_28104,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK2))) = sK22(sK1,relation_rng(sK2)) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_28059]) ).
tcf(c_28106,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_8158,c_28059]) ).
tcf(c_28108,plain,
( in(sK23(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_28059]) ).
tcf(c_28109,plain,
( in(sK24(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_28059]) ).
tcf(c_28113,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_28059]) ).
tcf(c_28118,plain,
( in(sK22(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_28059]) ).
tcf(c_28119,plain,
( in(sK21(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_28059]) ).
tcf(c_28120,plain,
( in(sK21(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_28059]) ).
tcf(c_28121,plain,
( in(sK22(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_28059]) ).
tcf(c_28122,plain,
( in(sK23(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_28059]) ).
tcf(c_28123,plain,
( in(sK24(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_28059]) ).
tcf(c_28130,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_28059]) ).
tcf(c_28132,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_28059]) ).
tcf(c_28135,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_28059]) ).
tcf(c_28136,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_28059]) ).
tcf(c_28456,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_28076]) ).
tcf(c_28464,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_28083]) ).
tcf(c_28467,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ in(X0,relation_rng(sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_23906,c_64,c_160,c_9882,c_23904]) ).
tcf(c_28474,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK2),X0),X0)
| ( relation_dom(relation_rng(sK2)) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_28467]) ).
tcf(c_28475,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_28467]) ).
tcf(c_28476,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ function(relation_rng(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_28467]) ).
tcf(c_28477,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK2),X0),X0)
| ( relation_rng(relation_rng(sK2)) = X0 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_28467]) ).
tcf(c_28478,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_rng(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_28467]) ).
tcf(c_28479,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0)
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_28467]) ).
tcf(c_28480,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK2)),sK21(X0,relation_rng(sK2))),X0)
| ( relation_inverse(X0) = relation_rng(sK2) )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_28467]) ).
tcf(c_28481,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_28467]) ).
tcf(c_28482,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)),X0)
| ( relation_rng(sK2) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_28467]) ).
tcf(c_28483,plain,
( empty(relation_rng(sK2))
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_3448,c_28467]) ).
tcf(c_28485,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_28467]) ).
tcf(c_28490,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK2))) = sK5(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5141,c_28467]) ).
tcf(c_28492,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_28467]) ).
tcf(c_28496,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = sK14(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5563,c_28467]) ).
tcf(c_28499,plain,
( in(sK23(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_28467]) ).
tcf(c_28500,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK2),sK1)) = sK23(relation_rng(sK2),sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_28467]) ).
tcf(c_28501,plain,
( in(sK24(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_28467]) ).
tcf(c_28502,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15109,c_28467]) ).
tcf(c_28503,plain,
( in(sK23(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_28467]) ).
tcf(c_28504,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK2))) = sK23(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_28467]) ).
tcf(c_28505,plain,
( in(sK24(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_28467]) ).
tcf(c_28506,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15119,c_28467]) ).
tcf(c_28507,plain,
( in(sK21(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_28467]) ).
tcf(c_28508,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK2),sK1)) = sK21(relation_rng(sK2),sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_28467]) ).
tcf(c_28509,plain,
( in(sK22(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_28467]) ).
tcf(c_28510,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1))
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_15124,c_28467]) ).
tcf(c_28511,plain,
( in(sK22(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_28467]) ).
tcf(c_28512,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK2))) = sK22(sK1,relation_rng(sK2)) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_28467]) ).
tcf(c_28513,plain,
( in(sK21(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_28467]) ).
tcf(c_28514,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8158,c_28467]) ).
tcf(c_28516,plain,
( in(sK23(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_28467]) ).
tcf(c_28517,plain,
( in(sK24(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_28467]) ).
tcf(c_28521,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_28467]) ).
tcf(c_28526,plain,
( in(sK22(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_28467]) ).
tcf(c_28527,plain,
( in(sK21(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_28467]) ).
tcf(c_28528,plain,
( in(sK21(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_28467]) ).
tcf(c_28529,plain,
( in(sK22(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_28467]) ).
tcf(c_28530,plain,
( in(sK23(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_28467]) ).
tcf(c_28531,plain,
( in(sK24(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_28467]) ).
tcf(c_28534,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18758,c_28467]) ).
tcf(c_28537,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_28467]) ).
tcf(c_28538,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_28467]) ).
tcf(c_28540,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_28467]) ).
tcf(c_28543,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_28467]) ).
tcf(c_28544,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(relation_dom(sK1))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_28467]) ).
tcf(c_28830,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_28094,c_3712,c_9966]) ).
tcf(c_28836,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_28830]) ).
tcf(c_28837,plain,
( ( relation_rng(sK2) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_28830]) ).
tcf(c_28865,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8770,c_87]) ).
tcf(c_28866,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8770,c_13488]) ).
tcf(c_28867,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8770,c_4623]) ).
tcf(c_28868,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8770,c_4763]) ).
tcf(c_28881,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_28865,c_4030]) ).
tcf(c_28882,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28881,c_987,c_3611]) ).
tcf(c_28915,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(X0)))) = relation_rng(relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3632]) ).
tcf(c_28916,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(X0)))) = relation_rng(relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3632]) ).
tcf(c_28917,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(X0)))) = relation_rng(relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3632]) ).
tcf(c_28918,plain,
relation_inverse(relation_inverse(relation_rng(empty_set))) = relation_rng(empty_set),
inference(superposition,[status(thm)],[c_136,c_3632]) ).
tcf(c_28919,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK1)))) = relation_rng(relation_inverse(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_3632]) ).
tcf(c_28920,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK1)))) = relation_rng(relation_dom(sK1)) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7619,c_3632]) ).
tcf(c_28921,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK2)))) = relation_rng(relation_inverse(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_3632]) ).
tcf(c_28922,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK2)))) = relation_rng(relation_rng(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_3632]) ).
tcf(c_28923,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK2)))) = relation_rng(relation_dom(sK2)) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_3632]) ).
tcf(c_28924,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0))))) = relation_rng(sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3632]) ).
tcf(c_28999,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3661]) ).
tcf(c_29000,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3661]) ).
tcf(c_29001,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3661]) ).
tcf(c_29002,plain,
! [X0: $i] :
( ( relation_dom(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_3661]) ).
tcf(c_29003,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_3661]) ).
tcf(c_29004,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7619,c_3661]) ).
tcf(c_29005,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9695,c_3661]) ).
tcf(c_29006,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9887,c_3661]) ).
tcf(c_29007,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4121,c_3661]) ).
tcf(c_29008,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3661]) ).
tcf(c_29046,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3662]) ).
tcf(c_29047,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3662]) ).
tcf(c_29048,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3662]) ).
tcf(c_29049,plain,
! [X0: $i] :
( ( relation_rng(empty_set) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_3662]) ).
tcf(c_29050,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_3662]) ).
tcf(c_29051,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7619,c_3662]) ).
tcf(c_29052,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9695,c_3662]) ).
tcf(c_29053,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9887,c_3662]) ).
tcf(c_29054,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4121,c_3662]) ).
tcf(c_29055,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3662]) ).
tcf(c_29126,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ~ empty(relation_rng(sK2))
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_22686,c_70]) ).
tcf(c_29127,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_69]) ).
tcf(c_29137,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_22656]) ).
tcf(c_29139,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_12701]) ).
tcf(c_29141,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_10144]) ).
tcf(c_29143,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_4468]) ).
tcf(c_29144,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK1) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_4215]) ).
tcf(c_29145,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_4216]) ).
tcf(c_29146,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_4201]) ).
tcf(c_29151,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_12622]) ).
tcf(c_29223,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(relation_rng(sK2))
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_22695,c_70]) ).
tcf(c_29224,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_69]) ).
tcf(c_29228,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_12284]) ).
tcf(c_29231,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_4619]) ).
tcf(c_29232,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_4406]) ).
tcf(c_29241,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| ( sK19(X0) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_4215]) ).
tcf(c_29242,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_4216]) ).
tcf(c_29243,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_4201]) ).
tcf(c_29248,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_10578]) ).
tcf(c_29326,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_28098,c_3712,c_9855,c_9888,c_27517]) ).
tcf(c_29332,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_29326]) ).
tcf(c_29333,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_29326]) ).
tcf(c_29375,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8771,c_87]) ).
tcf(c_29376,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8771,c_13488]) ).
tcf(c_29377,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8771,c_12807]) ).
tcf(c_29378,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8771,c_4623]) ).
tcf(c_29379,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8771,c_4763]) ).
tcf(c_29396,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_29375,c_4030]) ).
tcf(c_29397,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29396,c_987,c_3611]) ).
tcf(c_29432,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3663]) ).
tcf(c_29433,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3663]) ).
tcf(c_29434,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(X0)) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3663]) ).
tcf(c_29436,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4352,c_3663]) ).
tcf(c_29437,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK1)) = X0 )
| ~ empty(sK2)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_7619,c_3663]) ).
tcf(c_29438,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9695,c_3663]) ).
tcf(c_29439,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_9887,c_3663]) ).
tcf(c_29440,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK2)) = X0 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_4121,c_3663]) ).
tcf(c_29441,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3663]) ).
tcf(c_29448,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(light_normalisation,[status(thm)],[c_29438,c_3624]) ).
tcf(c_29562,plain,
( empty(relation_inverse(sK9))
| ~ relation(sK9)
| ~ empty(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_123,c_4366]) ).
tcf(c_29567,plain,
( empty(relation_inverse(sK9))
| ~ empty(relation_rng(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29562,c_83]) ).
tcf(c_29576,plain,
( empty(relation_inverse(sK9))
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_101,c_29567]) ).
tcf(c_29583,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_73,c_27525]) ).
tcf(c_29599,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK2 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29448]) ).
tcf(c_29600,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK2 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29448]) ).
tcf(c_29601,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK2 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29448]) ).
tcf(c_29604,plain,
( ( relation_dom(sK1) = sK2 )
| ~ empty(sK2)
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_7619,c_29448]) ).
tcf(c_29605,plain,
( ( relation_inverse(sK2) = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9695,c_29448]) ).
tcf(c_29606,plain,
( ( relation_rng(sK2) = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_9887,c_29448]) ).
tcf(c_29607,plain,
( ( relation_dom(sK2) = sK2 )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_4121,c_29448]) ).
tcf(c_29608,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = sK2 )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29448]) ).
tcf(c_29657,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_28102,c_3712,c_9855,c_9888,c_27521]) ).
tcf(c_29663,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(sK1) ),
inference(superposition,[status(thm)],[c_121,c_29657]) ).
tcf(c_29664,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4352,c_29657]) ).
tcf(c_29682,plain,
! [X0: $i] :
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11399,c_19431]) ).
tcf(c_29698,plain,
( ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK13(sK2,empty_set)) ),
inference(superposition,[status(thm)],[c_19961,c_70]) ).
tcf(c_29699,plain,
( element(sK13(sK2,empty_set),relation_rng(sK2))
| ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19961,c_69]) ).
tcf(c_29700,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(relation_rng(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19961,c_67]) ).
tcf(c_29720,plain,
( ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK6(sK2,empty_set)) ),
inference(superposition,[status(thm)],[c_20120,c_70]) ).
tcf(c_29721,plain,
( element(sK6(sK2,empty_set),relation_rng(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20120,c_69]) ).
tcf(c_29725,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(relation_dom(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20120,c_27478]) ).
tcf(c_29742,plain,
( ~ empty(relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(global_subsumption_just,[status(thm)],[c_22712,c_14937,c_22673]) ).
tcf(c_29743,plain,
( ( relation_inverse(sK1) = sK1 )
| ~ empty(relation_rng(sK2)) ),
inference(renaming,[status(thm)],[c_29742]) ).
tcf(c_29760,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8797,c_87]) ).
tcf(c_29761,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8797,c_13488]) ).
tcf(c_29762,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8797,c_4623]) ).
tcf(c_29763,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8797,c_4763]) ).
tcf(c_29776,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_29760,c_4030]) ).
tcf(c_29777,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29776,c_987,c_3611]) ).
tcf(c_29829,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4387,c_94]) ).
tcf(c_29836,plain,
! [X0: $i,X1: $i] :
( ( apply(X0,X1) = empty_set )
| ~ empty(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_29829]) ).
tcf(c_29837,plain,
! [X0: $i,X1: $i] :
( in(sK5(relation_dom(X0),X1),X1)
| ( relation_dom(relation_dom(X0)) = X1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_77,c_29829]) ).
tcf(c_29838,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(relation_dom(X1))
| ~ in(X0,relation_dom(relation_dom(X1))) ),
inference(superposition,[status(thm)],[c_79,c_29829]) ).
tcf(c_29839,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_87,c_29829]) ).
tcf(c_29840,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_dom(X0),X1),X1)
| ( relation_rng(relation_dom(X0)) = X1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_105,c_29829]) ).
tcf(c_29841,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(relation_dom(X1))
| ~ in(X0,relation_rng(relation_dom(X1))) ),
inference(superposition,[status(thm)],[c_107,c_29829]) ).
tcf(c_29842,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(relation_dom(X0),X1),sK22(relation_dom(X0),X1)),X1)
| ( relation_inverse(relation_dom(X0)) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_125,c_29829]) ).
tcf(c_29843,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,relation_dom(X0)),sK21(X1,relation_dom(X0))),X1)
| ( relation_dom(X0) = relation_inverse(X1) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_125,c_29829]) ).
tcf(c_29844,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,relation_dom(X0)),sK24(X1,relation_dom(X0))),X1)
| ( relation_dom(X0) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_130,c_29829]) ).
tcf(c_29845,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(relation_dom(X0),X1),sK24(relation_dom(X0),X1)),X1)
| ( relation_dom(X0) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_130,c_29829]) ).
tcf(c_29847,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_4546,c_29829]) ).
tcf(c_29848,plain,
! [X0: $i] :
( ~ empty(sK2)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_29829]) ).
tcf(c_29850,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_5275,c_29829]) ).
tcf(c_29851,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_29829]) ).
tcf(c_29852,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_29829]) ).
tcf(c_29853,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_29829]) ).
tcf(c_29854,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_29829]) ).
tcf(c_29855,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10732,c_29829]) ).
tcf(c_29856,plain,
! [X0: $i] :
( in(sK5(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_29829]) ).
tcf(c_29857,plain,
! [X0: $i] :
( in(sK6(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_29829]) ).
tcf(c_29858,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(X0))) = sK5(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_29829]) ).
tcf(c_29860,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_5335,c_29829]) ).
tcf(c_29861,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_29829]) ).
tcf(c_29862,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_29829]) ).
tcf(c_29863,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_29829]) ).
tcf(c_29864,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_29829]) ).
tcf(c_29865,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10736,c_29829]) ).
tcf(c_29866,plain,
! [X0: $i] :
( in(sK14(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_29829]) ).
tcf(c_29867,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(X0))) = sK14(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_29829]) ).
tcf(c_29868,plain,
! [X0: $i] :
( in(sK13(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_29829]) ).
tcf(c_29870,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_5542,c_29829]) ).
tcf(c_29872,plain,
! [X0: $i] :
( in(sK23(relation_dom(X0),sK1),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8327,c_29829]) ).
tcf(c_29873,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(X0),sK1)) = sK23(relation_dom(X0),sK1) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5709,c_29829]) ).
tcf(c_29874,plain,
! [X0: $i] :
( in(sK24(relation_dom(X0),sK1),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5669,c_29829]) ).
tcf(c_29875,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_15109,c_29829]) ).
tcf(c_29876,plain,
! [X0: $i] :
( in(sK23(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8322,c_29829]) ).
tcf(c_29877,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(X0))) = sK23(sK1,relation_dom(X0)) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5704,c_29829]) ).
tcf(c_29878,plain,
! [X0: $i] :
( in(sK24(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5654,c_29829]) ).
tcf(c_29879,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_15119,c_29829]) ).
tcf(c_29880,plain,
! [X0: $i] :
( in(sK21(relation_dom(X0),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8332,c_29829]) ).
tcf(c_29881,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(X0),sK1)) = sK21(relation_dom(X0),sK1) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5969,c_29829]) ).
tcf(c_29882,plain,
! [X0: $i] :
( in(sK22(relation_dom(X0),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5929,c_29829]) ).
tcf(c_29883,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_15124,c_29829]) ).
tcf(c_29884,plain,
! [X0: $i] :
( in(sK22(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8337,c_29829]) ).
tcf(c_29885,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(X0))) = sK22(sK1,relation_dom(X0)) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5964,c_29829]) ).
tcf(c_29886,plain,
! [X0: $i] :
( in(sK21(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_5914,c_29829]) ).
tcf(c_29888,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_7149,c_29829]) ).
tcf(c_29890,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ empty(sK2) ),
inference(superposition,[status(thm)],[c_6706,c_29829]) ).
tcf(c_29907,plain,
! [X0: $i] :
( in(sK23(sK2,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_23755,c_29829]) ).
tcf(c_29908,plain,
! [X0: $i] :
( in(sK24(sK2,relation_dom(X0)),relation_rng(sK2))
| ( relation_dom(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_18823,c_29829]) ).
tcf(c_29913,plain,
! [X0: $i] :
( in(sK5(sK2,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_29829]) ).
tcf(c_29914,plain,
! [X0: $i] :
( in(sK6(sK2,relation_dom(X0)),relation_rng(sK2))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_29829]) ).
tcf(c_29915,plain,
! [X0: $i] :
( in(sK14(sK2,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_29829]) ).
tcf(c_29916,plain,
! [X0: $i] :
( in(sK13(sK2,relation_dom(X0)),relation_rng(sK2))
| ( relation_dom(X0) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_29829]) ).
tcf(c_29917,plain,
! [X0: $i] :
( in(sK22(sK2,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_23773,c_29829]) ).
tcf(c_29918,plain,
! [X0: $i] :
( in(sK21(sK2,relation_dom(X0)),relation_rng(sK2))
| ( relation_dom(X0) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_18841,c_29829]) ).
tcf(c_29919,plain,
! [X0: $i] :
( in(sK21(relation_dom(X0),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_23767,c_29829]) ).
tcf(c_29920,plain,
! [X0: $i] :
( in(sK22(relation_dom(X0),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_18835,c_29829]) ).
tcf(c_29921,plain,
! [X0: $i] :
( in(sK23(relation_dom(X0),sK2),relation_dom(sK2))
| ( relation_dom(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_23761,c_29829]) ).
tcf(c_29922,plain,
! [X0: $i] :
( in(sK24(relation_dom(X0),sK2),relation_rng(sK2))
| ( relation_dom(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_18829,c_29829]) ).
tcf(c_29927,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_29829]) ).
tcf(c_29928,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_29829]) ).
tcf(c_29929,plain,
! [X0: $i] :
( ~ empty(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_29829]) ).
tcf(c_29930,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_29829]) ).
tcf(c_29932,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_29829]) ).
tcf(c_29934,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_29829]) ).
tcf(c_29937,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_29829]) ).
tcf(c_29938,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ in(X0,relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_29829]) ).
tcf(c_29940,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_29829]) ).
tcf(c_30414,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4448,c_94]) ).
tcf(c_30421,plain,
! [X0: $i,X1: $i] :
( in(sK5(relation_rng(X0),X1),X1)
| ( relation_dom(relation_rng(X0)) = X1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_77,c_30414]) ).
tcf(c_30422,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(relation_rng(X1))
| ~ in(X0,relation_dom(relation_rng(X1))) ),
inference(superposition,[status(thm)],[c_79,c_30414]) ).
tcf(c_30423,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(relation_rng(X1))
| ~ relation(relation_rng(X1))
| ~ in(X0,relation_dom(relation_rng(X1))) ),
inference(superposition,[status(thm)],[c_87,c_30414]) ).
tcf(c_30424,plain,
! [X0: $i,X1: $i] :
( in(sK13(relation_rng(X0),X1),X1)
| ( relation_rng(relation_rng(X0)) = X1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_105,c_30414]) ).
tcf(c_30425,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(relation_rng(X1))
| ~ in(X0,relation_rng(relation_rng(X1))) ),
inference(superposition,[status(thm)],[c_107,c_30414]) ).
tcf(c_30426,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(relation_rng(X0),X1),sK22(relation_rng(X0),X1)),X1)
| ( relation_inverse(relation_rng(X0)) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_125,c_30414]) ).
tcf(c_30427,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,relation_rng(X0)),sK21(X1,relation_rng(X0))),X1)
| ( relation_rng(X0) = relation_inverse(X1) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_125,c_30414]) ).
tcf(c_30428,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,relation_rng(X0)),sK24(X1,relation_rng(X0))),X1)
| ( relation_rng(X0) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_130,c_30414]) ).
tcf(c_30429,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(relation_rng(X0),X1),sK24(relation_rng(X0),X1)),X1)
| ( relation_rng(X0) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_130,c_30414]) ).
tcf(c_30431,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22686,c_30414]) ).
tcf(c_30432,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15072,c_30414]) ).
tcf(c_30433,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8549,c_30414]) ).
tcf(c_30434,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6287,c_30414]) ).
tcf(c_30435,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10732,c_30414]) ).
tcf(c_30436,plain,
! [X0: $i] :
( in(sK5(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_30414]) ).
tcf(c_30437,plain,
! [X0: $i] :
( in(sK6(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_30414]) ).
tcf(c_30438,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(X0))) = sK5(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_30414]) ).
tcf(c_30439,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_22695,c_30414]) ).
tcf(c_30440,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_15068,c_30414]) ).
tcf(c_30441,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8431,c_30414]) ).
tcf(c_30442,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ empty(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6337,c_30414]) ).
tcf(c_30443,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(sK1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_10736,c_30414]) ).
tcf(c_30444,plain,
! [X0: $i] :
( in(sK14(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_30414]) ).
tcf(c_30445,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(X0))) = sK14(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_30414]) ).
tcf(c_30446,plain,
! [X0: $i] :
( in(sK13(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_30414]) ).
tcf(c_30448,plain,
! [X0: $i] :
( in(sK23(relation_rng(X0),sK1),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8327,c_30414]) ).
tcf(c_30449,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(X0),sK1)) = sK23(relation_rng(X0),sK1) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5709,c_30414]) ).
tcf(c_30450,plain,
! [X0: $i] :
( in(sK24(relation_rng(X0),sK1),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5669,c_30414]) ).
tcf(c_30451,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_15109,c_30414]) ).
tcf(c_30452,plain,
! [X0: $i] :
( in(sK23(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8322,c_30414]) ).
tcf(c_30453,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(X0))) = sK23(sK1,relation_rng(X0)) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5704,c_30414]) ).
tcf(c_30454,plain,
! [X0: $i] :
( in(sK24(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5654,c_30414]) ).
tcf(c_30455,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = sK1 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_15119,c_30414]) ).
tcf(c_30456,plain,
! [X0: $i] :
( in(sK21(relation_rng(X0),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8332,c_30414]) ).
tcf(c_30457,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(X0)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(X0),sK1)) = sK21(relation_rng(X0),sK1) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5969,c_30414]) ).
tcf(c_30458,plain,
! [X0: $i] :
( in(sK22(relation_rng(X0),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(X0)) = sK1 )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5929,c_30414]) ).
tcf(c_30459,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ empty(relation_inverse(sK1))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_15124,c_30414]) ).
tcf(c_30460,plain,
! [X0: $i] :
( in(sK22(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8337,c_30414]) ).
tcf(c_30461,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(X0))) = sK22(sK1,relation_rng(X0)) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5964,c_30414]) ).
tcf(c_30462,plain,
! [X0: $i] :
( in(sK21(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5914,c_30414]) ).
tcf(c_30465,plain,
! [X0: $i] :
( in(sK23(sK2,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_23755,c_30414]) ).
tcf(c_30466,plain,
! [X0: $i] :
( in(sK24(sK2,relation_rng(X0)),relation_rng(sK2))
| ( relation_rng(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18823,c_30414]) ).
tcf(c_30467,plain,
! [X0: $i] :
( in(sK5(sK2,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_30414]) ).
tcf(c_30468,plain,
! [X0: $i] :
( in(sK6(sK2,relation_rng(X0)),relation_rng(sK2))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_30414]) ).
tcf(c_30470,plain,
! [X0: $i] :
( ~ empty(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_30414]) ).
tcf(c_30472,plain,
! [X0: $i] :
( in(sK14(sK2,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_30414]) ).
tcf(c_30473,plain,
! [X0: $i] :
( in(sK13(sK2,relation_rng(X0)),relation_rng(sK2))
| ( relation_rng(X0) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_30414]) ).
tcf(c_30475,plain,
! [X0: $i] :
( in(sK22(sK2,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_23773,c_30414]) ).
tcf(c_30476,plain,
! [X0: $i] :
( in(sK21(sK2,relation_rng(X0)),relation_rng(sK2))
| ( relation_rng(X0) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18841,c_30414]) ).
tcf(c_30477,plain,
! [X0: $i] :
( in(sK21(relation_rng(X0),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_23767,c_30414]) ).
tcf(c_30478,plain,
! [X0: $i] :
( in(sK22(relation_rng(X0),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(X0)) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18835,c_30414]) ).
tcf(c_30479,plain,
! [X0: $i] :
( in(sK23(relation_rng(X0),sK2),relation_dom(sK2))
| ( relation_rng(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_23761,c_30414]) ).
tcf(c_30480,plain,
! [X0: $i] :
( in(sK24(relation_rng(X0),sK2),relation_rng(sK2))
| ( relation_rng(X0) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18829,c_30414]) ).
tcf(c_30487,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_30414]) ).
tcf(c_30489,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_30414]) ).
tcf(c_30491,plain,
( ( relation_rng(sK2) = empty_set )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19961,c_30414]) ).
tcf(c_30492,plain,
( ( relation_dom(sK2) = empty_set )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20120,c_30414]) ).
tcf(c_30494,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_30414]) ).
tcf(c_30495,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ~ empty(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_30414]) ).
tcf(c_30499,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_30414]) ).
tcf(c_30500,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_30414]) ).
tcf(c_30501,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ in(X0,relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_30414]) ).
tcf(c_30801,plain,
( ~ empty(relation_dom(sK1))
| ~ in(sK4,relation_dom(sK1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_31399,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_8798,c_87]) ).
tcf(c_31400,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8798,c_13488]) ).
tcf(c_31401,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8798,c_12807]) ).
tcf(c_31402,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8798,c_4623]) ).
tcf(c_31403,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8798,c_4763]) ).
tcf(c_31420,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31399,c_4030]) ).
tcf(c_31421,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31420,c_987,c_3611]) ).
tcf(c_31454,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_5420,c_30414]) ).
tcf(c_31455,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ in(relation_rng(sK12),X0) ),
inference(superposition,[status(thm)],[c_5420,c_70]) ).
tcf(c_31456,plain,
! [X0: $i] :
( element(X0,relation_rng(sK12))
| ( apply(relation_inverse(sK12),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_69]) ).
tcf(c_31457,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_67]) ).
tcf(c_31458,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK12)) = X0 )
| ( apply(relation_inverse(sK12),ordered_pair(sK5(relation_rng(sK12),X0),X1)) = empty_set )
| ~ relation(relation_rng(sK12))
| ~ in(sK5(relation_rng(sK12),X0),X0) ),
inference(superposition,[status(thm)],[c_5420,c_76]) ).
tcf(c_31459,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_rng(sK12)))
| ( apply(relation_inverse(sK12),ordered_pair(X0,X1)) = empty_set )
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_106]) ).
tcf(c_31460,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_rng(sK12)))
| ( apply(relation_inverse(sK12),ordered_pair(X0,X1)) = empty_set )
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_78]) ).
tcf(c_31461,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_rng(sK12),X0) = X1 )
| ( apply(relation_inverse(sK12),ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_rng(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_197]) ).
tcf(c_31462,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK12)) = X0 )
| ( apply(relation_inverse(sK12),ordered_pair(X1,sK13(relation_rng(sK12),X0))) = empty_set )
| ~ relation(relation_rng(sK12))
| ~ in(sK13(relation_rng(sK12),X0),X0) ),
inference(superposition,[status(thm)],[c_5420,c_104]) ).
tcf(c_31463,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK12)) = X0 )
| ( apply(relation_inverse(sK12),ordered_pair(sK22(relation_rng(sK12),X0),sK21(relation_rng(sK12),X0))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_rng(sK12))
| ~ in(ordered_pair(sK21(relation_rng(sK12),X0),sK22(relation_rng(sK12),X0)),X0) ),
inference(superposition,[status(thm)],[c_5420,c_124]) ).
tcf(c_31464,plain,
! [X0: $i] :
( ( relation_rng(sK12) = X0 )
| ( apply(relation_inverse(sK12),ordered_pair(sK23(X0,relation_rng(sK12)),sK24(X0,relation_rng(sK12)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_rng(sK12))
| ~ in(ordered_pair(sK23(X0,relation_rng(sK12)),sK24(X0,relation_rng(sK12))),X0) ),
inference(superposition,[status(thm)],[c_5420,c_129]) ).
tcf(c_31465,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ( apply(relation_inverse(sK12),sK5(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_12622]) ).
tcf(c_31466,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ( apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_10578]) ).
tcf(c_31526,plain,
( empty(relation_inverse(sK9))
| ~ relation(sK9)
| ~ empty(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_123,c_7007]) ).
tcf(c_31531,plain,
( empty(relation_inverse(sK9))
| ~ empty(relation_dom(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31526,c_83]) ).
tcf(c_31588,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_9713,c_87]) ).
tcf(c_31589,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,sK7(sK1,X0)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_4726]) ).
tcf(c_31590,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_13488]) ).
tcf(c_31591,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_9713,c_12807]) ).
tcf(c_31592,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9713,c_4623]) ).
tcf(c_31593,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,apply(sK1,X0)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_4791]) ).
tcf(c_31594,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_9713,c_5251]) ).
tcf(c_31595,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9713,c_7241]) ).
tcf(c_31596,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_9713,c_7472]) ).
tcf(c_31597,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_6420]) ).
tcf(c_31598,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_6421]) ).
tcf(c_31599,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(sK1,sK6(sK1,empty_set)) = sK5(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8129]) ).
tcf(c_31600,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,sK13(sK1,empty_set)) = sK14(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8130]) ).
tcf(c_31601,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(empty_set,sK1)) = sK23(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8174]) ).
tcf(c_31602,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(sK1,empty_set)) = sK23(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8171]) ).
tcf(c_31603,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK22(empty_set,sK1)) = sK21(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_26641]) ).
tcf(c_31604,plain,
( ( relation_inverse(sK1) = empty_set )
| ( sK15(sK1,sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8177]) ).
tcf(c_31605,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8770]) ).
tcf(c_31606,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8771]) ).
tcf(c_31607,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8797]) ).
tcf(c_31608,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_8798]) ).
tcf(c_31646,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31588,c_4030]) ).
tcf(c_31647,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31646,c_987,c_3611]) ).
tcf(c_31719,plain,
( ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK14(sK2,empty_set)) ),
inference(superposition,[status(thm)],[c_24577,c_70]) ).
tcf(c_31720,plain,
( element(sK14(sK2,empty_set),relation_dom(sK2))
| ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_69]) ).
tcf(c_31723,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK14(sK2,empty_set))) = sK14(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_12701]) ).
tcf(c_31724,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK14(sK2,empty_set))) = sK14(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_10144]) ).
tcf(c_31725,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK14(sK2,empty_set)) = sK15(sK1,sK14(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_4468]) ).
tcf(c_31747,plain,
( ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK5(sK2,empty_set)) ),
inference(superposition,[status(thm)],[c_24805,c_70]) ).
tcf(c_31748,plain,
( element(sK5(sK2,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_69]) ).
tcf(c_31751,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK2,empty_set))) = sK5(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_12701]) ).
tcf(c_31752,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK2,empty_set))) = sK5(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_10144]) ).
tcf(c_31753,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK2,empty_set)) = sK15(sK1,sK5(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_4468]) ).
tcf(c_31775,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK2),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK2),X0),sK5(relation_inverse(sK2),X0)),sK2)
| ( relation_dom(relation_inverse(sK2)) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_3697]) ).
tcf(c_31776,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK2),X0),X0),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_3697]) ).
tcf(c_31777,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK2),X0),X0),sK2)
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_3697]) ).
tcf(c_31778,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK2),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK2),X0),sK14(relation_inverse(sK2),X0)),sK2)
| ( relation_rng(relation_inverse(sK2)) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_3697]) ).
tcf(c_31779,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK2),X0)),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_3697]) ).
tcf(c_31780,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),sK2)
| in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),X0)
| ( relation_inverse(relation_inverse(sK2)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_3697]) ).
tcf(c_31781,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_inverse(sK2)),sK21(X0,relation_inverse(sK2))),sK2)
| in(ordered_pair(sK22(X0,relation_inverse(sK2)),sK21(X0,relation_inverse(sK2))),X0)
| ( relation_inverse(X0) = relation_inverse(sK2) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_3697]) ).
tcf(c_31783,plain,
! [X0: $i] :
( in(ordered_pair(sK24(X0,relation_inverse(sK2)),sK23(X0,relation_inverse(sK2))),sK2)
| in(ordered_pair(sK23(X0,relation_inverse(sK2)),sK24(X0,relation_inverse(sK2))),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_3697]) ).
tcf(c_31784,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(sK2),X0),sK23(relation_inverse(sK2),X0)),sK2)
| in(ordered_pair(sK23(relation_inverse(sK2),X0),sK24(relation_inverse(sK2),X0)),X0)
| ( relation_inverse(sK2) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_3697]) ).
tcf(c_31786,plain,
( in(sK23(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(sK2),sK1),sK23(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_3697]) ).
tcf(c_31787,plain,
( in(ordered_pair(sK24(relation_inverse(sK2),sK1),sK23(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK2),sK1)) = sK23(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_3697]) ).
tcf(c_31788,plain,
( in(sK24(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK2),sK1),sK23(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_3697]) ).
tcf(c_31789,plain,
( in(sK23(sK1,relation_inverse(sK2)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(sK2)),sK23(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_3697]) ).
tcf(c_31790,plain,
( in(ordered_pair(sK24(sK1,relation_inverse(sK2)),sK23(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK2))) = sK23(sK1,relation_inverse(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_3697]) ).
tcf(c_31791,plain,
( in(sK24(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(sK2)),sK23(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_3697]) ).
tcf(c_31792,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_3697]) ).
tcf(c_31793,plain,
( in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(sK2),sK1)) = sK21(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_3697]) ).
tcf(c_31794,plain,
( in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_3697]) ).
tcf(c_31795,plain,
( in(sK22(sK1,relation_inverse(sK2)),relation_dom(sK1))
| in(ordered_pair(sK22(sK1,relation_inverse(sK2)),sK21(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_3697]) ).
tcf(c_31796,plain,
( in(ordered_pair(sK22(sK1,relation_inverse(sK2)),sK21(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_inverse(sK2))) = sK22(sK1,relation_inverse(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_3697]) ).
tcf(c_31797,plain,
( in(sK21(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(ordered_pair(sK22(sK1,relation_inverse(sK2)),sK21(sK1,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_3697]) ).
tcf(c_31798,plain,
( in(sK23(sK2,relation_inverse(sK2)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK2)),sK23(sK2,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_3697]) ).
tcf(c_31799,plain,
( in(sK24(sK2,relation_inverse(sK2)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK2)),sK23(sK2,relation_inverse(sK2))),sK2)
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_3697]) ).
tcf(c_31804,plain,
( in(sK23(relation_inverse(sK2),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK2),sK2),sK23(relation_inverse(sK2),sK2)),sK2)
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_3697]) ).
tcf(c_31805,plain,
( in(sK24(relation_inverse(sK2),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(sK2),sK2),sK23(relation_inverse(sK2),sK2)),sK2)
| ( relation_inverse(sK2) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_3697]) ).
tcf(c_31806,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK2),X0)),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31779,c_3845]) ).
tcf(c_31810,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK2),X0),X0),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31776,c_3805]) ).
tcf(c_31814,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK2),X0),X0),sK2)
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31777,c_3805]) ).
tcf(c_31851,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK2),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK2),X0),sK14(relation_inverse(sK2),X0)),sK2)
| ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31778,c_3845]) ).
tcf(c_31856,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK2),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK2),X0),sK5(relation_inverse(sK2),X0)),sK2)
| ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31775,c_3805]) ).
tcf(c_31869,plain,
( in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31794,c_3624]) ).
tcf(c_31874,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31792,c_3624]) ).
tcf(c_31891,plain,
( in(ordered_pair(sK21(relation_inverse(sK2),sK1),sK22(relation_inverse(sK2),sK1)),sK2)
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(sK2),sK1)) = sK21(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31793,c_3624]) ).
tcf(c_31911,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),sK2)
| in(ordered_pair(sK21(relation_inverse(sK2),X0),sK22(relation_inverse(sK2),X0)),X0)
| ( X0 = sK2 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31780,c_3624]) ).
tcf(c_31917,plain,
( in(sK3,relation_dom(sK2))
| ~ sP0(sK1,sK3,sK4,sK2)
| ( relation_inverse(sK1) != sK2 ) ),
inference(light_normalisation,[status(thm)],[c_4029,c_4013]) ).
tcf(c_31933,plain,
! [X0: $i] :
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11399,c_4045]) ).
tcf(c_31938,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),apply(sK2,X0)) = apply(sK1,apply(sK2,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_12284]) ).
tcf(c_31939,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,apply(sK2,X0))) = apply(sK2,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_4619]) ).
tcf(c_31940,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,apply(sK2,X0))) = apply(sK2,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_4406]) ).
tcf(c_32134,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK9),X0),X0)
| ( relation_dom(relation_rng(sK9)) = X0 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_77,c_29938]) ).
tcf(c_32135,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9))
| ~ in(X0,relation_dom(relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_79,c_29938]) ).
tcf(c_32136,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ function(relation_rng(sK9))
| ~ relation(relation_rng(sK9))
| ~ in(X0,relation_dom(relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_87,c_29938]) ).
tcf(c_32137,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK9),X0),X0)
| ( relation_rng(relation_rng(sK9)) = X0 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_105,c_29938]) ).
tcf(c_32138,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9))
| ~ in(X0,relation_rng(relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_107,c_29938]) ).
tcf(c_32139,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK9),X0),sK22(relation_rng(sK9),X0)),X0)
| ( relation_inverse(relation_rng(sK9)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_125,c_29938]) ).
tcf(c_32140,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK9)),sK21(X0,relation_rng(sK9))),X0)
| ( relation_inverse(X0) = relation_rng(sK9) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_125,c_29938]) ).
tcf(c_32141,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK9)),sK24(X0,relation_rng(sK9))),X0)
| ( relation_rng(sK9) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_130,c_29938]) ).
tcf(c_32142,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK9),X0),sK24(relation_rng(sK9),X0)),X0)
| ( relation_rng(sK9) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_130,c_29938]) ).
tcf(c_32144,plain,
( in(sK5(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8302,c_29938]) ).
tcf(c_32145,plain,
( in(sK6(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5335,c_29938]) ).
tcf(c_32146,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK9))) = sK5(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5141,c_29938]) ).
tcf(c_32147,plain,
( in(sK14(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8298,c_29938]) ).
tcf(c_32148,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK9))) = sK14(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5563,c_29938]) ).
tcf(c_32149,plain,
( in(sK13(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5542,c_29938]) ).
tcf(c_32150,plain,
( in(sK23(relation_rng(sK9),sK1),relation_dom(sK1))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_8327,c_29938]) ).
tcf(c_32151,plain,
( ( relation_rng(sK9) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK9),sK1)) = sK23(relation_rng(sK9),sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5709,c_29938]) ).
tcf(c_32152,plain,
( in(sK24(relation_rng(sK9),sK1),relation_dom(sK2))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5669,c_29938]) ).
tcf(c_32153,plain,
( in(sK23(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_8322,c_29938]) ).
tcf(c_32154,plain,
( ( relation_rng(sK9) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK9))) = sK23(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5704,c_29938]) ).
tcf(c_32155,plain,
( in(sK24(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5654,c_29938]) ).
tcf(c_32156,plain,
( in(sK21(relation_rng(sK9),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_8332,c_29938]) ).
tcf(c_32157,plain,
( ( relation_inverse(relation_rng(sK9)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK9),sK1)) = sK21(relation_rng(sK9),sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5969,c_29938]) ).
tcf(c_32158,plain,
( in(sK22(relation_rng(sK9),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5929,c_29938]) ).
tcf(c_32159,plain,
( in(sK22(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_8337,c_29938]) ).
tcf(c_32160,plain,
( ( relation_rng(sK9) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK9))) = sK22(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5964,c_29938]) ).
tcf(c_32161,plain,
( in(sK21(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_5914,c_29938]) ).
tcf(c_32162,plain,
( ( relation_rng(sK9) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8158,c_29938]) ).
tcf(c_32164,plain,
( in(sK23(sK2,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_23755,c_29938]) ).
tcf(c_32165,plain,
( in(sK24(sK2,relation_rng(sK9)),relation_rng(sK2))
| ( relation_rng(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_18823,c_29938]) ).
tcf(c_32166,plain,
( in(sK5(sK2,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_29938]) ).
tcf(c_32167,plain,
( in(sK6(sK2,relation_rng(sK9)),relation_rng(sK2))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_29938]) ).
tcf(c_32168,plain,
( in(sK14(sK2,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_rng(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_29938]) ).
tcf(c_32169,plain,
( in(sK13(sK2,relation_rng(sK9)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_rng(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_29938]) ).
tcf(c_32170,plain,
( in(sK22(sK2,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_23773,c_29938]) ).
tcf(c_32171,plain,
( in(sK21(sK2,relation_rng(sK9)),relation_rng(sK2))
| ( relation_rng(sK9) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_18841,c_29938]) ).
tcf(c_32172,plain,
( in(sK21(relation_rng(sK9),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK9)) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_23767,c_29938]) ).
tcf(c_32173,plain,
( in(sK22(relation_rng(sK9),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK9)) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_18835,c_29938]) ).
tcf(c_32174,plain,
( in(sK23(relation_rng(sK9),sK2),relation_dom(sK2))
| ( relation_rng(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_23761,c_29938]) ).
tcf(c_32175,plain,
( in(sK24(relation_rng(sK9),sK2),relation_rng(sK2))
| ( relation_rng(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_18829,c_29938]) ).
tcf(c_32403,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| in(sK6(sK1,powerset(X1)),relation_dom(sK2))
| ( powerset(X1) = relation_dom(sK1) )
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_6280,c_114]) ).
tcf(c_32404,plain,
! [X0: $i,X1: $i] :
( in(sK6(sK1,powerset(X1)),relation_dom(sK2))
| ( powerset(X1) = relation_dom(sK1) )
| ~ empty(X1)
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_6280,c_113]) ).
tcf(c_32405,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ in(relation_dom(sK2),sK6(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6280,c_70]) ).
tcf(c_32406,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_6280,c_69]) ).
tcf(c_32409,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6280,c_12701]) ).
tcf(c_32410,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6280,c_10144]) ).
tcf(c_32411,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6280,c_4468]) ).
tcf(c_32447,plain,
! [X0: $i] :
( element(sK6(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6286,c_30414]) ).
tcf(c_32448,plain,
! [X0: $i] :
( element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6286,c_70]) ).
tcf(c_32451,plain,
! [X0: $i] :
( element(sK6(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6286,c_29829]) ).
tcf(c_32456,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6286,c_12701]) ).
tcf(c_32457,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6286,c_10144]) ).
tcf(c_32458,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_6286,c_4468]) ).
tcf(c_32459,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| element(sK6(sK1,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_6286,c_4215]) ).
tcf(c_32460,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| element(sK6(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_6286,c_4216]) ).
tcf(c_32461,plain,
! [X0: $i] :
( element(sK6(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6286,c_4201]) ).
tcf(c_32462,plain,
( element(sK6(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6286,c_29938]) ).
tcf(c_32463,plain,
! [X0: $i] :
( element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6286,c_12622]) ).
tcf(c_32511,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| in(sK13(sK1,powerset(X1)),relation_dom(sK2))
| ( powerset(X1) = relation_dom(sK2) )
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_6330,c_114]) ).
tcf(c_32512,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK1,powerset(X1)),relation_dom(sK2))
| ( powerset(X1) = relation_dom(sK2) )
| ~ empty(X1)
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_6330,c_113]) ).
tcf(c_32513,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ in(relation_dom(sK2),sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6330,c_70]) ).
tcf(c_32514,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_6330,c_69]) ).
tcf(c_32517,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6330,c_12701]) ).
tcf(c_32518,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6330,c_10144]) ).
tcf(c_32519,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6330,c_4468]) ).
tcf(c_32521,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_6330,c_10148]) ).
tcf(c_32561,plain,
! [X0: $i] :
( element(sK13(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6336,c_30414]) ).
tcf(c_32562,plain,
! [X0: $i] :
( element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6336,c_70]) ).
tcf(c_32565,plain,
! [X0: $i] :
( element(sK13(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6336,c_29829]) ).
tcf(c_32566,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_6336,c_12284]) ).
tcf(c_32567,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_6336,c_4619]) ).
tcf(c_32568,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_6336,c_4406]) ).
tcf(c_32573,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| element(sK13(sK1,sK19(X0)),relation_dom(sK2))
| ( sK19(X0) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_6336,c_4215]) ).
tcf(c_32574,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| element(sK13(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_6336,c_4216]) ).
tcf(c_32575,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),relation_dom(sK2))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6336,c_4201]) ).
tcf(c_32576,plain,
( element(sK13(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6336,c_29938]) ).
tcf(c_32577,plain,
! [X0: $i] :
( element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6336,c_10578]) ).
tcf(c_32618,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6473,c_94,c_6473]) ).
tcf(c_32626,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(sK1,X0)) ),
inference(superposition,[status(thm)],[c_32618,c_70]) ).
tcf(c_32627,plain,
! [X0: $i] :
( element(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_69]) ).
tcf(c_32630,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_12701]) ).
tcf(c_32631,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_10144]) ).
tcf(c_32632,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK15(sK1,sK24(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_4468]) ).
tcf(c_32648,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6563,c_94,c_6563]) ).
tcf(c_32656,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(X0,sK1)) ),
inference(superposition,[status(thm)],[c_32648,c_70]) ).
tcf(c_32657,plain,
! [X0: $i] :
( element(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_69]) ).
tcf(c_32660,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_12701]) ).
tcf(c_32661,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_10144]) ).
tcf(c_32662,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK15(sK1,sK24(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_4468]) ).
tcf(c_32686,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK15(sK1,sK13(sK1,empty_set))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_9987,c_87]) ).
tcf(c_32687,plain,
( in(ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9987,c_13488]) ).
tcf(c_32688,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_9987,c_12807]) ).
tcf(c_32689,plain,
( in(ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9987,c_4623]) ).
tcf(c_32690,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,sK13(sK1,empty_set)) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_9987,c_8130]) ).
tcf(c_32702,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK15(sK1,sK13(sK1,empty_set))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_32686,c_4030]) ).
tcf(c_32703,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK15(sK1,sK13(sK1,empty_set))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32702,c_987,c_3611]) ).
tcf(c_32752,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK12),X0),X0)
| ( relation_dom(relation_rng(sK12)) = X0 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_29940]) ).
tcf(c_32753,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_dom(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_79,c_29940]) ).
tcf(c_32754,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ function(relation_rng(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_dom(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_87,c_29940]) ).
tcf(c_32755,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK12),X0),X0)
| ( relation_rng(relation_rng(sK12)) = X0 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_29940]) ).
tcf(c_32756,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_rng(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_107,c_29940]) ).
tcf(c_32757,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK12),X0),sK22(relation_rng(sK12),X0)),X0)
| ( relation_inverse(relation_rng(sK12)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_29940]) ).
tcf(c_32758,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK12)),sK21(X0,relation_rng(sK12))),X0)
| ( relation_inverse(X0) = relation_rng(sK12) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_29940]) ).
tcf(c_32759,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK12)),sK24(X0,relation_rng(sK12))),X0)
| ( relation_rng(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_29940]) ).
tcf(c_32760,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK12),X0),sK24(relation_rng(sK12),X0)),X0)
| ( relation_rng(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_29940]) ).
tcf(c_32762,plain,
( element(sK6(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_6286,c_29940]) ).
tcf(c_32763,plain,
( in(sK5(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8302,c_29940]) ).
tcf(c_32764,plain,
( in(sK6(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5335,c_29940]) ).
tcf(c_32765,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5141,c_29940]) ).
tcf(c_32766,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_29940]) ).
tcf(c_32767,plain,
( element(sK13(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_6336,c_29940]) ).
tcf(c_32768,plain,
( in(sK14(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8298,c_29940]) ).
tcf(c_32769,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5563,c_29940]) ).
tcf(c_32770,plain,
( in(sK13(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5542,c_29940]) ).
tcf(c_32771,plain,
( in(sK23(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_29940]) ).
tcf(c_32772,plain,
( ( relation_rng(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK12),sK1)) = sK23(relation_rng(sK12),sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_29940]) ).
tcf(c_32773,plain,
( in(sK24(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_29940]) ).
tcf(c_32774,plain,
( in(sK23(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_29940]) ).
tcf(c_32775,plain,
( ( relation_rng(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK12))) = sK23(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_29940]) ).
tcf(c_32776,plain,
( in(sK24(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_29940]) ).
tcf(c_32777,plain,
( in(sK21(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_29940]) ).
tcf(c_32778,plain,
( ( relation_inverse(relation_rng(sK12)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK12),sK1)) = sK21(relation_rng(sK12),sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_29940]) ).
tcf(c_32779,plain,
( in(sK22(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_29940]) ).
tcf(c_32780,plain,
( in(sK22(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_29940]) ).
tcf(c_32781,plain,
( ( relation_rng(sK12) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK12))) = sK22(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_29940]) ).
tcf(c_32782,plain,
( in(sK21(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_29940]) ).
tcf(c_32783,plain,
( ( relation_rng(sK12) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8158,c_29940]) ).
tcf(c_32785,plain,
( in(sK23(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23755,c_29940]) ).
tcf(c_32786,plain,
( in(sK24(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18823,c_29940]) ).
tcf(c_32787,plain,
( in(sK5(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_29940]) ).
tcf(c_32788,plain,
( in(sK6(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_29940]) ).
tcf(c_32789,plain,
( in(sK14(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_rng(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_29940]) ).
tcf(c_32790,plain,
( in(sK13(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_rng(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_29940]) ).
tcf(c_32791,plain,
( in(sK22(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23773,c_29940]) ).
tcf(c_32792,plain,
( in(sK21(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18841,c_29940]) ).
tcf(c_32793,plain,
( in(sK21(relation_rng(sK12),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23767,c_29940]) ).
tcf(c_32794,plain,
( in(sK22(relation_rng(sK12),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18835,c_29940]) ).
tcf(c_32795,plain,
( in(sK23(relation_rng(sK12),sK2),relation_dom(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23761,c_29940]) ).
tcf(c_32796,plain,
( in(sK24(relation_rng(sK12),sK2),relation_rng(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18829,c_29940]) ).
tcf(c_32981,plain,
! [X0: $i] :
( ( apply(sK12,X0) = empty_set )
| ~ function(sK12)
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_89,c_30499]) ).
tcf(c_32982,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK12),X0),X0)
| ( relation_dom(relation_dom(sK12)) = X0 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_30499]) ).
tcf(c_32983,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_dom(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_79,c_30499]) ).
tcf(c_32984,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ function(relation_dom(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_dom(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_87,c_30499]) ).
tcf(c_32985,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK12),X0),X0)
| ( relation_rng(relation_dom(sK12)) = X0 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_30499]) ).
tcf(c_32986,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_rng(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_107,c_30499]) ).
tcf(c_32987,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK12),X0),sK22(relation_dom(sK12),X0)),X0)
| ( relation_inverse(relation_dom(sK12)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_30499]) ).
tcf(c_32988,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK12)),sK21(X0,relation_dom(sK12))),X0)
| ( relation_inverse(X0) = relation_dom(sK12) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_30499]) ).
tcf(c_32989,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK12)),sK24(X0,relation_dom(sK12))),X0)
| ( relation_dom(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_30499]) ).
tcf(c_32990,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK12),X0),sK24(relation_dom(sK12),X0)),X0)
| ( relation_dom(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_30499]) ).
tcf(c_32992,plain,
( element(sK6(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_6286,c_30499]) ).
tcf(c_32993,plain,
( in(sK5(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8302,c_30499]) ).
tcf(c_32994,plain,
( in(sK6(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5335,c_30499]) ).
tcf(c_32995,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5141,c_30499]) ).
tcf(c_32996,plain,
( element(sK13(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_6336,c_30499]) ).
tcf(c_32997,plain,
( in(sK14(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8298,c_30499]) ).
tcf(c_32998,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5563,c_30499]) ).
tcf(c_32999,plain,
( in(sK13(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5542,c_30499]) ).
tcf(c_33000,plain,
( in(sK23(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_30499]) ).
tcf(c_33001,plain,
( ( relation_dom(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK12),sK1)) = sK23(relation_dom(sK12),sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_30499]) ).
tcf(c_33002,plain,
( in(sK24(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_30499]) ).
tcf(c_33003,plain,
( in(sK23(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_30499]) ).
tcf(c_33004,plain,
( ( relation_dom(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK12))) = sK23(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_30499]) ).
tcf(c_33005,plain,
( in(sK24(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_30499]) ).
tcf(c_33006,plain,
( in(sK21(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_30499]) ).
tcf(c_33007,plain,
( ( relation_inverse(relation_dom(sK12)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK12),sK1)) = sK21(relation_dom(sK12),sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_30499]) ).
tcf(c_33008,plain,
( in(sK22(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_30499]) ).
tcf(c_33009,plain,
( in(sK22(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK12) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_30499]) ).
tcf(c_33010,plain,
( ( relation_dom(sK12) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK12))) = sK22(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_30499]) ).
tcf(c_33011,plain,
( in(sK21(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_30499]) ).
tcf(c_33012,plain,
( ( relation_dom(sK12) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8158,c_30499]) ).
tcf(c_33014,plain,
( in(sK23(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23755,c_30499]) ).
tcf(c_33015,plain,
( in(sK24(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18823,c_30499]) ).
tcf(c_33016,plain,
( in(sK5(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_30499]) ).
tcf(c_33017,plain,
( in(sK6(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_30499]) ).
tcf(c_33018,plain,
( in(sK14(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_30499]) ).
tcf(c_33019,plain,
( in(sK13(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_30499]) ).
tcf(c_33020,plain,
( in(sK22(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23773,c_30499]) ).
tcf(c_33021,plain,
( in(sK21(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK12) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18841,c_30499]) ).
tcf(c_33022,plain,
( in(sK21(relation_dom(sK12),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23767,c_30499]) ).
tcf(c_33023,plain,
( in(sK22(relation_dom(sK12),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18835,c_30499]) ).
tcf(c_33024,plain,
( in(sK23(relation_dom(sK12),sK2),relation_dom(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23761,c_30499]) ).
tcf(c_33025,plain,
( in(sK24(relation_dom(sK12),sK2),relation_rng(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18829,c_30499]) ).
tcf(c_33034,plain,
! [X0: $i] :
( ( apply(sK12,X0) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32981,c_96,c_95]) ).
tcf(c_33295,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| in(sK14(sK1,powerset(X1)),relation_dom(sK1))
| ( powerset(X1) = relation_dom(sK2) )
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_8422,c_114]) ).
tcf(c_33296,plain,
! [X0: $i,X1: $i] :
( in(sK14(sK1,powerset(X1)),relation_dom(sK1))
| ( powerset(X1) = relation_dom(sK2) )
| ~ empty(X1)
| ~ in(X0,sK13(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_8422,c_113]) ).
tcf(c_33297,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ~ in(relation_dom(sK1),sK14(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8422,c_70]) ).
tcf(c_33298,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 ) ),
inference(superposition,[status(thm)],[c_8422,c_69]) ).
tcf(c_33301,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK14(sK1,X0)) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8422,c_12284]) ).
tcf(c_33302,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8422,c_4619]) ).
tcf(c_33303,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8422,c_4406]) ).
tcf(c_33339,plain,
! [X0: $i] :
( element(sK14(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8430,c_30414]) ).
tcf(c_33340,plain,
! [X0: $i] :
( element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ~ in(X0,sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8430,c_70]) ).
tcf(c_33343,plain,
! [X0: $i] :
( element(sK14(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8430,c_29829]) ).
tcf(c_33344,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8430,c_12284]) ).
tcf(c_33345,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8430,c_4619]) ).
tcf(c_33346,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8430,c_4406]) ).
tcf(c_33351,plain,
! [X0: $i] :
( empty(X0)
| element(sK13(sK1,sK19(X0)),X0)
| element(sK14(sK1,sK19(X0)),relation_dom(sK1))
| ( sK19(X0) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8430,c_4215]) ).
tcf(c_33352,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(powerset(X0))),X0)
| element(sK14(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8430,c_4216]) ).
tcf(c_33353,plain,
! [X0: $i] :
( element(sK14(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8430,c_4201]) ).
tcf(c_33354,plain,
( element(sK14(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8430,c_29938]) ).
tcf(c_33355,plain,
( element(sK14(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8430,c_29940]) ).
tcf(c_33356,plain,
! [X0: $i] :
( element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8430,c_10578]) ).
tcf(c_33358,plain,
( element(sK14(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8430,c_30499]) ).
tcf(c_33411,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| in(sK5(sK1,powerset(X1)),relation_dom(sK1))
| ( powerset(X1) = relation_dom(sK1) )
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_8540,c_114]) ).
tcf(c_33412,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK1,powerset(X1)),relation_dom(sK1))
| ( powerset(X1) = relation_dom(sK1) )
| ~ empty(X1)
| ~ in(X0,sK5(sK1,powerset(X1))) ),
inference(superposition,[status(thm)],[c_8540,c_113]) ).
tcf(c_33413,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ in(relation_dom(sK1),sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8540,c_70]) ).
tcf(c_33414,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| element(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 ) ),
inference(superposition,[status(thm)],[c_8540,c_69]) ).
tcf(c_33417,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK5(sK1,X0)) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8540,c_12284]) ).
tcf(c_33418,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8540,c_4619]) ).
tcf(c_33419,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8540,c_4406]) ).
tcf(c_33421,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_8540,c_12287]) ).
tcf(c_33464,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_10032,c_87]) ).
tcf(c_33465,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10032,c_9713]) ).
tcf(c_33466,plain,
( in(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10032,c_13488]) ).
tcf(c_33467,plain,
( in(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10032,c_4623]) ).
tcf(c_33468,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10032,c_4763]) ).
tcf(c_33481,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_33464,c_4030]) ).
tcf(c_33482,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33481,c_987,c_3611]) ).
tcf(c_33508,plain,
! [X0: $i] :
( ( apply(sK12,X0) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_33034]) ).
tcf(c_33520,plain,
! [X0: $i] :
( ( apply(sK9,X0) = empty_set )
| ~ function(sK9)
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_89,c_30501]) ).
tcf(c_33521,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK9),X0),X0)
| ( relation_dom(relation_dom(sK9)) = X0 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_77,c_30501]) ).
tcf(c_33522,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9))
| ~ in(X0,relation_dom(relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_79,c_30501]) ).
tcf(c_33523,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ function(relation_dom(sK9))
| ~ relation(relation_dom(sK9))
| ~ in(X0,relation_dom(relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_87,c_30501]) ).
tcf(c_33524,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK9),X0),X0)
| ( relation_rng(relation_dom(sK9)) = X0 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_105,c_30501]) ).
tcf(c_33525,plain,
! [X0: $i] :
( ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9))
| ~ in(X0,relation_rng(relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_107,c_30501]) ).
tcf(c_33526,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK9),X0),sK22(relation_dom(sK9),X0)),X0)
| ( relation_inverse(relation_dom(sK9)) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_125,c_30501]) ).
tcf(c_33527,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK9)),sK21(X0,relation_dom(sK9))),X0)
| ( relation_inverse(X0) = relation_dom(sK9) )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_125,c_30501]) ).
tcf(c_33528,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK9)),sK24(X0,relation_dom(sK9))),X0)
| ( relation_dom(sK9) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_130,c_30501]) ).
tcf(c_33529,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK9),X0),sK24(relation_dom(sK9),X0)),X0)
| ( relation_dom(sK9) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_130,c_30501]) ).
tcf(c_33531,plain,
( element(sK6(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6286,c_30501]) ).
tcf(c_33532,plain,
( in(sK5(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8302,c_30501]) ).
tcf(c_33533,plain,
( in(sK6(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5335,c_30501]) ).
tcf(c_33534,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK9))) = sK5(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5141,c_30501]) ).
tcf(c_33535,plain,
( element(sK14(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8430,c_30501]) ).
tcf(c_33536,plain,
( element(sK13(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6336,c_30501]) ).
tcf(c_33537,plain,
( in(sK14(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8298,c_30501]) ).
tcf(c_33538,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK9))) = sK14(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5563,c_30501]) ).
tcf(c_33539,plain,
( in(sK13(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_5542,c_30501]) ).
tcf(c_33540,plain,
( in(sK23(relation_dom(sK9),sK1),relation_dom(sK1))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_8327,c_30501]) ).
tcf(c_33541,plain,
( ( relation_dom(sK9) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK9),sK1)) = sK23(relation_dom(sK9),sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5709,c_30501]) ).
tcf(c_33542,plain,
( in(sK24(relation_dom(sK9),sK1),relation_dom(sK2))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5669,c_30501]) ).
tcf(c_33543,plain,
( in(sK23(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_8322,c_30501]) ).
tcf(c_33544,plain,
( ( relation_dom(sK9) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK9))) = sK23(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5704,c_30501]) ).
tcf(c_33545,plain,
( in(sK24(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5654,c_30501]) ).
tcf(c_33546,plain,
( in(sK21(relation_dom(sK9),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_8332,c_30501]) ).
tcf(c_33547,plain,
( ( relation_inverse(relation_dom(sK9)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK9),sK1)) = sK21(relation_dom(sK9),sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5969,c_30501]) ).
tcf(c_33548,plain,
( in(sK22(relation_dom(sK9),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5929,c_30501]) ).
tcf(c_33549,plain,
( in(sK22(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK9) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_8337,c_30501]) ).
tcf(c_33550,plain,
( ( relation_dom(sK9) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK9))) = sK22(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5964,c_30501]) ).
tcf(c_33551,plain,
( in(sK21(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK9) = relation_inverse(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_5914,c_30501]) ).
tcf(c_33552,plain,
( ( relation_dom(sK9) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8158,c_30501]) ).
tcf(c_33554,plain,
( in(sK23(sK2,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_23755,c_30501]) ).
tcf(c_33555,plain,
( in(sK24(sK2,relation_dom(sK9)),relation_rng(sK2))
| ( relation_dom(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_18823,c_30501]) ).
tcf(c_33556,plain,
( in(sK5(sK2,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_30501]) ).
tcf(c_33557,plain,
( in(sK6(sK2,relation_dom(sK9)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_30501]) ).
tcf(c_33558,plain,
( in(sK14(sK2,relation_dom(sK9)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_30501]) ).
tcf(c_33559,plain,
( in(sK13(sK2,relation_dom(sK9)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_30501]) ).
tcf(c_33560,plain,
( in(sK22(sK2,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK9) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_23773,c_30501]) ).
tcf(c_33561,plain,
( in(sK21(sK2,relation_dom(sK9)),relation_rng(sK2))
| ( relation_dom(sK9) = relation_inverse(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_18841,c_30501]) ).
tcf(c_33562,plain,
( in(sK21(relation_dom(sK9),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK9)) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_23767,c_30501]) ).
tcf(c_33563,plain,
( in(sK22(relation_dom(sK9),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK9)) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_18835,c_30501]) ).
tcf(c_33564,plain,
( in(sK23(relation_dom(sK9),sK2),relation_dom(sK2))
| ( relation_dom(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_23761,c_30501]) ).
tcf(c_33565,plain,
( in(sK24(relation_dom(sK9),sK2),relation_rng(sK2))
| ( relation_dom(sK9) = sK2 )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_18829,c_30501]) ).
tcf(c_33574,plain,
! [X0: $i] :
( ( apply(sK9,X0) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33520,c_84,c_83]) ).
tcf(c_33754,plain,
( ( relation_rng(sK9) = empty_set )
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_32162]) ).
tcf(c_33761,plain,
( ( relation_rng(sK12) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_32783]) ).
tcf(c_33770,plain,
! [X0: $i] :
( element(sK5(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8548,c_30414]) ).
tcf(c_33771,plain,
! [X0: $i] :
( element(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ~ in(X0,sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8548,c_70]) ).
tcf(c_33774,plain,
! [X0: $i] :
( element(sK5(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8548,c_29829]) ).
tcf(c_33779,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8548,c_12701]) ).
tcf(c_33780,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8548,c_10144]) ).
tcf(c_33781,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8548,c_4468]) ).
tcf(c_33782,plain,
! [X0: $i] :
( empty(X0)
| element(sK5(sK1,sK19(X0)),X0)
| element(sK5(sK1,sK19(X0)),relation_dom(sK1))
| ( sK19(X0) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8548,c_4215]) ).
tcf(c_33783,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),X0)
| element(sK5(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8548,c_4216]) ).
tcf(c_33784,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(powerset(X0))),relation_dom(sK1))
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8548,c_4201]) ).
tcf(c_33785,plain,
( element(sK5(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8548,c_29938]) ).
tcf(c_33786,plain,
! [X0: $i] :
( element(sK5(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8548,c_12622]) ).
tcf(c_33787,plain,
( element(sK5(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8548,c_29940]) ).
tcf(c_33789,plain,
( element(sK5(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8548,c_30499]) ).
tcf(c_33790,plain,
( element(sK5(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8548,c_30501]) ).
tcf(c_33839,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_8858,c_94,c_8858]) ).
tcf(c_33847,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(sK1,X0)) ),
inference(superposition,[status(thm)],[c_33839,c_70]) ).
tcf(c_33848,plain,
! [X0: $i] :
( element(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_69]) ).
tcf(c_33851,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK23(sK1,X0)) = apply(sK1,sK23(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_12284]) ).
tcf(c_33852,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_4619]) ).
tcf(c_33853,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_4406]) ).
tcf(c_33869,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_8977,c_94,c_8977]) ).
tcf(c_33877,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(X0,sK1)) ),
inference(superposition,[status(thm)],[c_33869,c_70]) ).
tcf(c_33878,plain,
! [X0: $i] :
( element(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_69]) ).
tcf(c_33881,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK23(X0,sK1)) = apply(sK1,sK23(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_12284]) ).
tcf(c_33882,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_4619]) ).
tcf(c_33883,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_4406]) ).
tcf(c_33962,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10201,c_87]) ).
tcf(c_33963,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10201,c_4863]) ).
tcf(c_33967,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10201,c_4791]) ).
tcf(c_33974,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33962,c_65,c_64]) ).
tcf(c_33997,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_33974,c_4410,c_4546]) ).
tcf(c_34004,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_33997,c_70]) ).
tcf(c_34005,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_33997,c_69]) ).
tcf(c_34007,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_33997,c_106]) ).
tcf(c_34010,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_33997,c_104]) ).
tcf(c_34011,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_33997,c_4259]) ).
tcf(c_34013,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_33997,c_3784]) ).
tcf(c_34016,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_34007,c_4013]) ).
tcf(c_34024,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0) ),
inference(light_normalisation,[status(thm)],[c_34010,c_4013]) ).
tcf(c_34034,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(relation_dom(sK1),sK7(relation_inverse(sK1),X0)) ),
inference(superposition,[status(thm)],[c_34011,c_70]) ).
tcf(c_34035,plain,
! [X0: $i] :
( element(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34011,c_69]) ).
tcf(c_34038,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( sK15(relation_inverse(sK1),sK7(relation_inverse(sK1),X0)) = apply(sK1,sK7(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34011,c_12284]) ).
tcf(c_34039,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34011,c_4619]) ).
tcf(c_34040,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34011,c_4406]) ).
tcf(c_34065,plain,
( in(ordered_pair(sK7(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_10033,c_87]) ).
tcf(c_34066,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,sK7(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_9713]) ).
tcf(c_34067,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10033,c_13488]) ).
tcf(c_34068,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK7(sK1,sK14(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_12807]) ).
tcf(c_34069,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10033,c_4623]) ).
tcf(c_34070,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(sK1,sK7(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_4763]) ).
tcf(c_34086,plain,
( in(ordered_pair(sK7(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_34065,c_4030]) ).
tcf(c_34087,plain,
( in(ordered_pair(sK7(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34086,c_987,c_3611]) ).
tcf(c_34112,plain,
! [X0: $i] :
( ( apply(sK9,X0) = empty_set )
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_33574]) ).
tcf(c_34124,plain,
( ( relation_dom(sK12) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_121,c_33012]) ).
tcf(c_34131,plain,
( ( relation_dom(sK9) = empty_set )
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_33552]) ).
tcf(c_34199,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(relation_dom(X0))) = relation_inverse(relation_dom(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11024]) ).
tcf(c_34200,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(relation_rng(X0))) = relation_inverse(relation_dom(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11024]) ).
tcf(c_34201,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(relation_inverse(X0))) = relation_inverse(relation_dom(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11024]) ).
tcf(c_34202,plain,
function_inverse(relation_dom(empty_set)) = relation_inverse(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_136,c_11024]) ).
tcf(c_34203,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(X0)))) = relation_inverse(relation_dom(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11024]) ).
tcf(c_34217,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(relation_dom(X0))) = relation_inverse(relation_rng(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11025]) ).
tcf(c_34218,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(relation_rng(X0))) = relation_inverse(relation_rng(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11025]) ).
tcf(c_34219,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(relation_inverse(X0))) = relation_inverse(relation_rng(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11025]) ).
tcf(c_34220,plain,
function_inverse(relation_rng(empty_set)) = relation_inverse(relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_136,c_11025]) ).
tcf(c_34221,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(X0)))) = relation_inverse(relation_rng(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11025]) ).
tcf(c_34235,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(relation_dom(X0))) = relation_inverse(relation_inverse(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_11026]) ).
tcf(c_34236,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(relation_rng(X0))) = relation_inverse(relation_inverse(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_11026]) ).
tcf(c_34237,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(relation_inverse(X0))) = relation_inverse(relation_inverse(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_11026]) ).
tcf(c_34238,plain,
function_inverse(relation_inverse(empty_set)) = relation_inverse(relation_inverse(empty_set)),
inference(superposition,[status(thm)],[c_136,c_11026]) ).
tcf(c_34239,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(X0)))) = relation_inverse(relation_inverse(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_11026]) ).
tcf(c_34255,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12148]) ).
tcf(c_34256,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12148]) ).
tcf(c_34257,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12148]) ).
tcf(c_34258,plain,
relation_rng(sK20(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12148]) ).
tcf(c_34259,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12148]) ).
tcf(c_34273,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12149]) ).
tcf(c_34274,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12149]) ).
tcf(c_34275,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12149]) ).
tcf(c_34276,plain,
relation_dom(sK20(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12149]) ).
tcf(c_34277,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12149]) ).
tcf(c_34291,plain,
( element(sK20(empty_set),empty_set)
| empty(sK20(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_14781,c_13142]) ).
tcf(c_34292,plain,
! [X0: $i] :
( empty(X0)
| empty(sK20(powerset(X0)))
| in(sK20(sK20(powerset(X0))),X0) ),
inference(superposition,[status(thm)],[c_13142,c_68]) ).
tcf(c_34293,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK20(powerset(powerset(X1))))
| ~ in(X0,sK20(sK20(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_13142,c_114]) ).
tcf(c_34294,plain,
! [X0: $i,X1: $i] :
( empty(sK20(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK20(sK20(powerset(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_13142,c_113]) ).
tcf(c_34295,plain,
( empty(empty_set)
| element(sK20(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_34291,c_14781]) ).
tcf(c_34339,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4726,c_12764]) ).
tcf(c_34340,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_9713,c_12764]) ).
tcf(c_34344,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_12764]) ).
tcf(c_34345,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_12764]) ).
tcf(c_34346,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_12764]) ).
tcf(c_34347,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_12764]) ).
tcf(c_34348,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_12764]) ).
tcf(c_34350,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_9987,c_12764]) ).
tcf(c_34351,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK13(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8130,c_12764]) ).
tcf(c_34352,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK24(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8174,c_12764]) ).
tcf(c_34353,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK24(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8171,c_12764]) ).
tcf(c_34354,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_26641,c_12764]) ).
tcf(c_34355,plain,
( ( relation_inverse(sK1) = empty_set )
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8177,c_12764]) ).
tcf(c_34356,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8771,c_12764]) ).
tcf(c_34357,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8798,c_12764]) ).
tcf(c_34358,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK7(sK1,sK14(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_12764]) ).
tcf(c_34363,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12764,c_87]) ).
tcf(c_34403,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34363,c_65,c_64]) ).
tcf(c_34529,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_34403,c_4546,c_4623]) ).
tcf(c_34536,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4726,c_34529]) ).
tcf(c_34537,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_9713,c_34529]) ).
tcf(c_34538,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_4763,c_34529]) ).
tcf(c_34539,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4791,c_34529]) ).
tcf(c_34543,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_34529]) ).
tcf(c_34544,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_34529]) ).
tcf(c_34545,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_34529]) ).
tcf(c_34546,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_34529]) ).
tcf(c_34547,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6420,c_34529]) ).
tcf(c_34548,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_34529]) ).
tcf(c_34550,plain,
( in(ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9987,c_34529]) ).
tcf(c_34551,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8130,c_34529]) ).
tcf(c_34552,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8174,c_34529]) ).
tcf(c_34553,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8171,c_34529]) ).
tcf(c_34554,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_26641,c_34529]) ).
tcf(c_34555,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1)
| ( relation_inverse(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8177,c_34529]) ).
tcf(c_34556,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8770,c_34529]) ).
tcf(c_34557,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8771,c_34529]) ).
tcf(c_34558,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8797,c_34529]) ).
tcf(c_34559,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8798,c_34529]) ).
tcf(c_34560,plain,
( in(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10032,c_34529]) ).
tcf(c_34561,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_34529]) ).
tcf(c_34564,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),X0),X0)) ),
inference(superposition,[status(thm)],[c_34529,c_70]) ).
tcf(c_34565,plain,
! [X0: $i] :
( element(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34529,c_69]) ).
tcf(c_34571,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34529,c_4259]) ).
tcf(c_34680,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4840,c_34537]) ).
tcf(c_34681,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4863,c_34537]) ).
tcf(c_34682,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,X0),X0)) ),
inference(superposition,[status(thm)],[c_34537,c_70]) ).
tcf(c_34683,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34537,c_69]) ).
tcf(c_34689,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34537,c_4259]) ).
tcf(c_34715,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4726,c_34571]) ).
tcf(c_34717,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_4763,c_34571]) ).
tcf(c_34718,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4791,c_34571]) ).
tcf(c_34722,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_34571]) ).
tcf(c_34723,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_34571]) ).
tcf(c_34724,plain,
( in(sK15(sK1,sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_34571]) ).
tcf(c_34725,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_34571]) ).
tcf(c_34726,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6420,c_34571]) ).
tcf(c_34727,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_34571]) ).
tcf(c_34729,plain,
( in(sK15(sK1,sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9987,c_34571]) ).
tcf(c_34743,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(relation_dom(sK1),apply(relation_inverse(sK1),X0)) ),
inference(superposition,[status(thm)],[c_34571,c_70]) ).
tcf(c_34744,plain,
! [X0: $i] :
( element(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34571,c_69]) ).
tcf(c_34747,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( sK15(relation_inverse(sK1),apply(relation_inverse(sK1),X0)) = apply(sK1,apply(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34571,c_12284]) ).
tcf(c_34748,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34571,c_4619]) ).
tcf(c_34749,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34571,c_4406]) ).
tcf(c_34817,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4726,c_34565]) ).
tcf(c_34819,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_4763,c_34565]) ).
tcf(c_34820,plain,
! [X0: $i] :
( element(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4791,c_34565]) ).
tcf(c_34824,plain,
( element(ordered_pair(sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5251,c_34565]) ).
tcf(c_34825,plain,
( element(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7241,c_34565]) ).
tcf(c_34826,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_34565]) ).
tcf(c_34827,plain,
( element(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_34565]) ).
tcf(c_34828,plain,
( element(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6420,c_34565]) ).
tcf(c_34829,plain,
( element(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_6421,c_34565]) ).
tcf(c_34831,plain,
( element(ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_9987,c_34565]) ).
tcf(c_34832,plain,
( element(ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8130,c_34565]) ).
tcf(c_34833,plain,
( element(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8174,c_34565]) ).
tcf(c_34834,plain,
( element(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8171,c_34565]) ).
tcf(c_34835,plain,
( element(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_26641,c_34565]) ).
tcf(c_34836,plain,
( element(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1)
| ( relation_inverse(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8177,c_34565]) ).
tcf(c_34837,plain,
( element(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8770,c_34565]) ).
tcf(c_34838,plain,
( element(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8771,c_34565]) ).
tcf(c_34839,plain,
( element(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8797,c_34565]) ).
tcf(c_34840,plain,
( element(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8798,c_34565]) ).
tcf(c_34841,plain,
( element(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10032,c_34565]) ).
tcf(c_34842,plain,
( element(ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10033,c_34565]) ).
tcf(c_35022,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15878]) ).
tcf(c_35023,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15878]) ).
tcf(c_35024,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15878]) ).
tcf(c_35025,plain,
relation_dom(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15878]) ).
tcf(c_35026,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15878]) ).
tcf(c_35040,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15879]) ).
tcf(c_35041,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15879]) ).
tcf(c_35042,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15879]) ).
tcf(c_35043,plain,
relation_dom(relation_dom(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15879]) ).
tcf(c_35044,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15879]) ).
tcf(c_35058,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15880]) ).
tcf(c_35059,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15880]) ).
tcf(c_35060,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15880]) ).
tcf(c_35061,plain,
relation_dom(relation_dom(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15880]) ).
tcf(c_35062,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15880]) ).
tcf(c_35186,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15915]) ).
tcf(c_35187,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15915]) ).
tcf(c_35188,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15915]) ).
tcf(c_35189,plain,
relation_dom(relation_dom(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15915]) ).
tcf(c_35190,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15915]) ).
tcf(c_35216,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_11399,c_19430]) ).
tcf(c_35233,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15916]) ).
tcf(c_35234,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15916]) ).
tcf(c_35235,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15916]) ).
tcf(c_35236,plain,
relation_dom(relation_dom(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15916]) ).
tcf(c_35237,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15916]) ).
tcf(c_35251,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15917]) ).
tcf(c_35252,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15917]) ).
tcf(c_35253,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15917]) ).
tcf(c_35254,plain,
relation_dom(relation_dom(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15917]) ).
tcf(c_35255,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15917]) ).
tcf(c_35269,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15950]) ).
tcf(c_35270,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15950]) ).
tcf(c_35271,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15950]) ).
tcf(c_35272,plain,
relation_dom(relation_dom(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15950]) ).
tcf(c_35273,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15950]) ).
tcf(c_35287,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15951]) ).
tcf(c_35288,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15951]) ).
tcf(c_35289,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15951]) ).
tcf(c_35290,plain,
relation_dom(relation_dom(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15951]) ).
tcf(c_35291,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15951]) ).
tcf(c_35318,plain,
( in(sK5(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK9)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_29856]) ).
tcf(c_35320,plain,
( in(sK5(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK12)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_29856]) ).
tcf(c_35321,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK5(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_29856,c_70]) ).
tcf(c_35325,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_dom(X0))) = apply(sK1,sK5(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_12284]) ).
tcf(c_35326,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(X0)))) = sK5(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_4619]) ).
tcf(c_35327,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(X0)))) = sK5(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_4406]) ).
tcf(c_35329,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(sK5(sK1,relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_29856,c_12287]) ).
tcf(c_35356,plain,
( in(sK6(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK9)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_29857]) ).
tcf(c_35358,plain,
( in(sK6(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK12)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_29857]) ).
tcf(c_35359,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK6(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_29857,c_70]) ).
tcf(c_35363,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_dom(X0)))) = sK6(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_12701]) ).
tcf(c_35364,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_dom(X0)))) = sK6(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_10144]) ).
tcf(c_35365,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(X0))) = sK15(sK1,sK6(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_4468]) ).
tcf(c_35387,plain,
( in(sK14(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(empty_set) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3404,c_29866]) ).
tcf(c_35389,plain,
( in(sK14(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK9)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_29866]) ).
tcf(c_35391,plain,
( in(sK14(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK12)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_29866]) ).
tcf(c_35392,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK14(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_29866,c_70]) ).
tcf(c_35396,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_dom(X0))) = apply(sK1,sK14(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_12284]) ).
tcf(c_35397,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(X0)))) = sK14(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_4619]) ).
tcf(c_35398,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(X0)))) = sK14(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_4406]) ).
tcf(c_35399,plain,
( in(sK14(sK1,empty_set),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_35387,c_3404]) ).
tcf(c_35422,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(empty_set) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3404,c_29868]) ).
tcf(c_35424,plain,
( in(sK13(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK9)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_29868]) ).
tcf(c_35426,plain,
( in(sK13(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK12)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_29868]) ).
tcf(c_35427,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK13(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_29868,c_70]) ).
tcf(c_35431,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_dom(X0)))) = sK13(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_12701]) ).
tcf(c_35432,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_dom(X0)))) = sK13(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_10144]) ).
tcf(c_35433,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(X0))) = sK15(sK1,sK13(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_4468]) ).
tcf(c_35435,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(sK13(sK1,relation_dom(X0)),relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_29868,c_10148]) ).
tcf(c_35436,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_35422,c_3404]) ).
tcf(c_35466,plain,
( in(sK5(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK12)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_30436]) ).
tcf(c_35468,plain,
( in(sK5(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK9)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_30436]) ).
tcf(c_35470,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK5(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_30436,c_70]) ).
tcf(c_35474,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_rng(X0))) = apply(sK1,sK5(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_12284]) ).
tcf(c_35475,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(X0)))) = sK5(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_4619]) ).
tcf(c_35476,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(X0)))) = sK5(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_4406]) ).
tcf(c_35477,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(sK5(sK1,relation_rng(X0)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_30436,c_12287]) ).
tcf(c_35504,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_87]) ).
tcf(c_35505,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10207,c_4863]) ).
tcf(c_35506,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(relation_dom(sK2),sK5(sK1,relation_dom(sK2)))
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_6246]) ).
tcf(c_35507,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_6247]) ).
tcf(c_35508,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_5332]) ).
tcf(c_35509,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10207,c_4791]) ).
tcf(c_35530,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35504,c_65,c_64]) ).
tcf(c_35571,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_15952]) ).
tcf(c_35572,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_15952]) ).
tcf(c_35573,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15952]) ).
tcf(c_35574,plain,
relation_dom(relation_dom(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15952]) ).
tcf(c_35575,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_15952]) ).
tcf(c_35610,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_16053]) ).
tcf(c_35611,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_16053]) ).
tcf(c_35612,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_16053]) ).
tcf(c_35613,plain,
relation_dom(relation_rng(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_16053]) ).
tcf(c_35614,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_16053]) ).
tcf(c_35628,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_16054]) ).
tcf(c_35629,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_16054]) ).
tcf(c_35630,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_16054]) ).
tcf(c_35631,plain,
relation_dom(relation_rng(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_16054]) ).
tcf(c_35632,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_16054]) ).
tcf(c_35646,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_16055]) ).
tcf(c_35647,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_16055]) ).
tcf(c_35648,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_16055]) ).
tcf(c_35649,plain,
relation_dom(relation_rng(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_16055]) ).
tcf(c_35650,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_16055]) ).
tcf(c_35668,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_35530,c_70]) ).
tcf(c_35669,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35530,c_69]) ).
tcf(c_35671,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35530,c_106]) ).
tcf(c_35676,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35530,c_3784]) ).
tcf(c_35677,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_35671,c_4013]) ).
tcf(c_35700,plain,
( in(sK6(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK12)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_30437]) ).
tcf(c_35702,plain,
( in(sK6(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK9)) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_30437]) ).
tcf(c_35704,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK6(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_30437,c_70]) ).
tcf(c_35708,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_rng(X0)))) = sK6(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_12701]) ).
tcf(c_35709,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_rng(X0)))) = sK6(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_10144]) ).
tcf(c_35710,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(X0))) = sK15(sK1,sK6(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_4468]) ).
tcf(c_35747,plain,
( in(sK14(sK1,empty_set),relation_dom(sK1))
| ( relation_rng(empty_set) = relation_dom(sK2) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3424,c_30444]) ).
tcf(c_35748,plain,
( in(sK14(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK12)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_30444]) ).
tcf(c_35750,plain,
( in(sK14(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK9)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_30444]) ).
tcf(c_35752,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK14(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_30444,c_70]) ).
tcf(c_35756,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_rng(X0))) = apply(sK1,sK14(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_12284]) ).
tcf(c_35757,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(X0)))) = sK14(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_4619]) ).
tcf(c_35758,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(X0)))) = sK14(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_4406]) ).
tcf(c_35802,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_rng(empty_set) = relation_dom(sK2) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3424,c_30446]) ).
tcf(c_35803,plain,
( in(sK13(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK12)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_30446]) ).
tcf(c_35805,plain,
( in(sK13(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK9)) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_30446]) ).
tcf(c_35807,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK13(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_30446,c_70]) ).
tcf(c_35811,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_rng(X0)))) = sK13(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_12701]) ).
tcf(c_35812,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_rng(X0)))) = sK13(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_10144]) ).
tcf(c_35813,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(X0))) = sK15(sK1,sK13(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_4468]) ).
tcf(c_35814,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(sK13(sK1,relation_rng(X0)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_30446,c_10148]) ).
tcf(c_35856,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10226,c_87]) ).
tcf(c_35857,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10226,c_4863]) ).
tcf(c_35861,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK7(relation_inverse(sK1),sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10226,c_4791]) ).
tcf(c_35870,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35856,c_65,c_64]) ).
tcf(c_35907,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17543]) ).
tcf(c_35908,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17543]) ).
tcf(c_35909,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17543]) ).
tcf(c_35910,plain,
relation_dom(relation_rng(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17543]) ).
tcf(c_35911,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17543]) ).
tcf(c_35979,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17544]) ).
tcf(c_35980,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17544]) ).
tcf(c_35981,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17544]) ).
tcf(c_35982,plain,
relation_dom(relation_rng(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17544]) ).
tcf(c_35983,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17544]) ).
tcf(c_35997,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17545]) ).
tcf(c_35998,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17545]) ).
tcf(c_35999,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17545]) ).
tcf(c_36000,plain,
relation_dom(relation_rng(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17545]) ).
tcf(c_36001,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17545]) ).
tcf(c_36023,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17578]) ).
tcf(c_36024,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17578]) ).
tcf(c_36025,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17578]) ).
tcf(c_36026,plain,
relation_dom(relation_rng(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17578]) ).
tcf(c_36027,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17578]) ).
tcf(c_36104,plain,
! [X0: $i] :
( empty(X0)
| element(sK20(sK19(X0)),X0) ),
inference(global_subsumption_just,[status(thm)],[c_15176,c_118,c_15176]) ).
tcf(c_36111,plain,
! [X0: $i] :
( empty(X0)
| in(sK20(sK19(X0)),X0) ),
inference(superposition,[status(thm)],[c_36104,c_68]) ).
tcf(c_36112,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK20(sK19(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_36104,c_114]) ).
tcf(c_36113,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK20(sK19(powerset(X1)))) ),
inference(superposition,[status(thm)],[c_36104,c_113]) ).
tcf(c_36116,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK20(sK19(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36113,c_137]) ).
tcf(c_36119,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK20(sK19(powerset(X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36112,c_137]) ).
tcf(c_36132,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_35870,c_70]) ).
tcf(c_36133,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35870,c_69]) ).
tcf(c_36135,plain,
( in(sK22(sK1,sK1),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35870,c_106]) ).
tcf(c_36140,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK7(relation_inverse(sK1),sK22(sK1,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_35870,c_3784]) ).
tcf(c_36141,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_36135,c_4013]) ).
tcf(c_36174,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(X0,sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_4726,c_34564]) ).
tcf(c_36177,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(X0,apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_4791,c_34564]) ).
tcf(c_36181,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK1,ordered_pair(sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_5251,c_34564]) ).
tcf(c_36182,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK1,ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_7241,c_34564]) ).
tcf(c_36183,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_7060,c_34564]) ).
tcf(c_36184,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK1,ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_7472,c_34564]) ).
tcf(c_36185,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_6420,c_34564]) ).
tcf(c_36186,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_6421,c_34564]) ).
tcf(c_36188,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_9987,c_34564]) ).
tcf(c_36189,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_8130,c_34564]) ).
tcf(c_36190,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_8174,c_34564]) ).
tcf(c_36191,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_8171,c_34564]) ).
tcf(c_36192,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_26641,c_34564]) ).
tcf(c_36193,plain,
( ( relation_inverse(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_8177,c_34564]) ).
tcf(c_36194,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1)))) ),
inference(superposition,[status(thm)],[c_8770,c_34564]) ).
tcf(c_36195,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1)))) ),
inference(superposition,[status(thm)],[c_8771,c_34564]) ).
tcf(c_36196,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1)))) ),
inference(superposition,[status(thm)],[c_8797,c_34564]) ).
tcf(c_36197,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1)))) ),
inference(superposition,[status(thm)],[c_8798,c_34564]) ).
tcf(c_36198,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_10032,c_34564]) ).
tcf(c_36199,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_10033,c_34564]) ).
tcf(c_36354,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_6671,c_94,c_6671]) ).
tcf(c_36362,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK21(sK1,X0)) ),
inference(superposition,[status(thm)],[c_36354,c_70]) ).
tcf(c_36363,plain,
! [X0: $i] :
( element(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_69]) ).
tcf(c_36366,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_12701]) ).
tcf(c_36367,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_10144]) ).
tcf(c_36368,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK15(sK1,sK21(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_4468]) ).
tcf(c_36472,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10228,c_87]) ).
tcf(c_36473,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10228,c_4863]) ).
tcf(c_36477,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK7(relation_inverse(sK1),sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10228,c_4791]) ).
tcf(c_36486,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36472,c_65,c_64]) ).
tcf(c_36515,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK20(sK19(X0))) ),
inference(superposition,[status(thm)],[c_36111,c_70]) ).
tcf(c_36519,plain,
( empty(relation_dom(sK1))
| ( sK15(relation_inverse(sK1),sK20(sK19(relation_dom(sK1)))) = apply(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_12284]) ).
tcf(c_36520,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_36111,c_4619]) ).
tcf(c_36521,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_36111,c_4406]) ).
tcf(c_36523,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(relation_inverse(sK1),sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_36111,c_12701]) ).
tcf(c_36524,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_36111,c_10144]) ).
tcf(c_36525,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK20(sK19(relation_dom(sK2)))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_4468]) ).
tcf(c_36526,plain,
! [X0: $i] :
( empty(X0)
| empty(sK19(X0))
| element(sK20(sK19(sK19(X0))),X0) ),
inference(superposition,[status(thm)],[c_36111,c_4215]) ).
tcf(c_36527,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| element(sK20(sK19(sK20(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_36111,c_4216]) ).
tcf(c_36557,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(sK19(powerset(X0))),X1),X1)
| ( relation_dom(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_77,c_36116]) ).
tcf(c_36558,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_dom(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_79,c_36116]) ).
tcf(c_36559,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(sK20(sK19(powerset(X1))))
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_dom(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_87,c_36116]) ).
tcf(c_36560,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(sK19(powerset(X0))),X1),X1)
| ( relation_rng(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_105,c_36116]) ).
tcf(c_36561,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_rng(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_107,c_36116]) ).
tcf(c_36562,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(sK20(sK19(powerset(X0))),X1),sK22(sK20(sK19(powerset(X0))),X1)),X1)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_125,c_36116]) ).
tcf(c_36563,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,sK20(sK19(powerset(X0)))),sK21(X1,sK20(sK19(powerset(X0))))),X1)
| ( sK20(sK19(powerset(X0))) = relation_inverse(X1) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_125,c_36116]) ).
tcf(c_36564,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,sK20(sK19(powerset(X0)))),sK24(X1,sK20(sK19(powerset(X0))))),X1)
| ( sK20(sK19(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_130,c_36116]) ).
tcf(c_36565,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(sK20(sK19(powerset(X0))),X1),sK24(sK20(sK19(powerset(X0))),X1)),X1)
| ( sK20(sK19(powerset(X0))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_130,c_36116]) ).
tcf(c_36567,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8548,c_36116]) ).
tcf(c_36568,plain,
! [X0: $i] :
( element(sK6(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6286,c_36116]) ).
tcf(c_36569,plain,
! [X0: $i] :
( in(sK5(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_36116]) ).
tcf(c_36570,plain,
! [X0: $i] :
( in(sK6(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_36116]) ).
tcf(c_36571,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(sK19(powerset(X0))))) = sK5(sK1,sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_36116]) ).
tcf(c_36572,plain,
! [X0: $i] :
( element(sK14(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8430,c_36116]) ).
tcf(c_36573,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6336,c_36116]) ).
tcf(c_36574,plain,
! [X0: $i] :
( in(sK14(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_36116]) ).
tcf(c_36575,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(sK19(powerset(X0))))) = sK14(sK1,sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_36116]) ).
tcf(c_36576,plain,
! [X0: $i] :
( in(sK13(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_36116]) ).
tcf(c_36577,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(powerset(X0))),sK1),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8327,c_36116]) ).
tcf(c_36578,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(sK19(powerset(X0))),sK1)) = sK23(sK20(sK19(powerset(X0))),sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5709,c_36116]) ).
tcf(c_36579,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(powerset(X0))),sK1),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5669,c_36116]) ).
tcf(c_36580,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8322,c_36116]) ).
tcf(c_36581,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(sK19(powerset(X0))))) = sK23(sK1,sK20(sK19(powerset(X0)))) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5704,c_36116]) ).
tcf(c_36582,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5654,c_36116]) ).
tcf(c_36583,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(powerset(X0))),sK1),relation_dom(sK1))
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8332,c_36116]) ).
tcf(c_36584,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(sK19(powerset(X0))),sK1)) = sK21(sK20(sK19(powerset(X0))),sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5969,c_36116]) ).
tcf(c_36585,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(powerset(X0))),sK1),relation_dom(sK2))
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5929,c_36116]) ).
tcf(c_36586,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8337,c_36116]) ).
tcf(c_36587,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(sK19(powerset(X0))))) = sK22(sK1,sK20(sK19(powerset(X0)))) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5964,c_36116]) ).
tcf(c_36588,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5914,c_36116]) ).
tcf(c_36589,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(X0))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8158,c_36116]) ).
tcf(c_36591,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23755,c_36116]) ).
tcf(c_36592,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18823,c_36116]) ).
tcf(c_36593,plain,
! [X0: $i] :
( in(sK5(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_36116]) ).
tcf(c_36594,plain,
! [X0: $i] :
( in(sK6(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_36116]) ).
tcf(c_36595,plain,
! [X0: $i] :
( in(sK14(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_36116]) ).
tcf(c_36596,plain,
! [X0: $i] :
( in(sK13(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_36116]) ).
tcf(c_36597,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23773,c_36116]) ).
tcf(c_36598,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18841,c_36116]) ).
tcf(c_36599,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(powerset(X0))),sK2),relation_dom(sK2))
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23767,c_36116]) ).
tcf(c_36600,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(powerset(X0))),sK2),relation_rng(sK2))
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18835,c_36116]) ).
tcf(c_36601,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(powerset(X0))),sK2),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23761,c_36116]) ).
tcf(c_36602,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(powerset(X0))),sK2),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18829,c_36116]) ).
tcf(c_36603,plain,
! [X0: $i] :
( empty(sK20(sK19(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36111,c_36116]) ).
tcf(c_36892,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(sK19(powerset(X0))),X1),X1)
| element(ordered_pair(sK5(sK20(sK19(powerset(X0))),X1),sK6(sK20(sK19(powerset(X0))),X1)),X0)
| ( relation_dom(sK20(sK19(powerset(X0)))) = X1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_77,c_36119]) ).
tcf(c_36893,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK7(sK20(sK19(powerset(X1))),X0)),X1)
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_dom(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_79,c_36119]) ).
tcf(c_36894,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(sK20(sK19(powerset(X1))),X0)),X1)
| ~ function(sK20(sK19(powerset(X1))))
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_dom(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_87,c_36119]) ).
tcf(c_36895,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(sK19(powerset(X0))),X1),X1)
| element(ordered_pair(sK14(sK20(sK19(powerset(X0))),X1),sK13(sK20(sK19(powerset(X0))),X1)),X0)
| ( relation_rng(sK20(sK19(powerset(X0)))) = X1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_105,c_36119]) ).
tcf(c_36896,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK15(sK20(sK19(powerset(X1))),X0),X0),X1)
| ~ relation(sK20(sK19(powerset(X1))))
| ~ in(X0,relation_rng(sK20(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_107,c_36119]) ).
tcf(c_36897,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK22(sK20(sK19(powerset(X0))),X1),sK21(sK20(sK19(powerset(X0))),X1)),X0)
| in(ordered_pair(sK21(sK20(sK19(powerset(X0))),X1),sK22(sK20(sK19(powerset(X0))),X1)),X1)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_125,c_36119]) ).
tcf(c_36898,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK21(X1,sK20(sK19(powerset(X0)))),sK22(X1,sK20(sK19(powerset(X0))))),X0)
| in(ordered_pair(sK22(X1,sK20(sK19(powerset(X0)))),sK21(X1,sK20(sK19(powerset(X0))))),X1)
| ( sK20(sK19(powerset(X0))) = relation_inverse(X1) )
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_125,c_36119]) ).
tcf(c_36899,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(X1,sK20(sK19(powerset(X0)))),sK24(X1,sK20(sK19(powerset(X0))))),X0)
| in(ordered_pair(sK23(X1,sK20(sK19(powerset(X0)))),sK24(X1,sK20(sK19(powerset(X0))))),X1)
| ( sK20(sK19(powerset(X0))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_130,c_36119]) ).
tcf(c_36900,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(sK20(sK19(powerset(X0))),X1),sK24(sK20(sK19(powerset(X0))),X1)),X0)
| in(ordered_pair(sK23(sK20(sK19(powerset(X0))),X1),sK24(sK20(sK19(powerset(X0))),X1)),X1)
| ( sK20(sK19(powerset(X0))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_130,c_36119]) ).
tcf(c_36901,plain,
! [X0: $i] :
( empty(sK20(sK19(powerset(X0))))
| element(sK20(sK20(sK19(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_3448,c_36119]) ).
tcf(c_36902,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),X0)
| element(sK5(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8548,c_36119]) ).
tcf(c_36903,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),X0)
| element(sK6(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_6286,c_36119]) ).
tcf(c_36904,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),X0)
| in(sK5(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8302,c_36119]) ).
tcf(c_36905,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),X0)
| in(sK6(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_5335,c_36119]) ).
tcf(c_36906,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(powerset(X0)))),X0)
| ( sK20(sK19(powerset(X0))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(sK19(powerset(X0))))) = sK5(sK1,sK20(sK19(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_5141,c_36119]) ).
tcf(c_36907,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),X0)
| element(sK14(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8430,c_36119]) ).
tcf(c_36908,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),X0)
| element(sK13(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_6336,c_36119]) ).
tcf(c_36909,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),X0)
| in(sK14(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8298,c_36119]) ).
tcf(c_36910,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),X0)
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(sK19(powerset(X0))))) = sK14(sK1,sK20(sK19(powerset(X0)))) ) ),
inference(superposition,[status(thm)],[c_5563,c_36119]) ).
tcf(c_36911,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(powerset(X0)))),X0)
| in(sK13(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_5542,c_36119]) ).
tcf(c_36912,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(powerset(X0))),sK1),relation_dom(sK1))
| element(ordered_pair(sK23(sK20(sK19(powerset(X0))),sK1),sK24(sK20(sK19(powerset(X0))),sK1)),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8327,c_36119]) ).
tcf(c_36913,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK20(sK19(powerset(X0))),sK1),sK24(sK20(sK19(powerset(X0))),sK1)),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(sK19(powerset(X0))),sK1)) = sK23(sK20(sK19(powerset(X0))),sK1) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5709,c_36119]) ).
tcf(c_36914,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(powerset(X0))),sK1),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(sK19(powerset(X0))),sK1),sK24(sK20(sK19(powerset(X0))),sK1)),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5669,c_36119]) ).
tcf(c_36915,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| element(ordered_pair(sK23(sK1,sK20(sK19(powerset(X0)))),sK24(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8322,c_36119]) ).
tcf(c_36916,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,sK20(sK19(powerset(X0)))),sK24(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(sK19(powerset(X0))))) = sK23(sK1,sK20(sK19(powerset(X0)))) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5704,c_36119]) ).
tcf(c_36917,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| element(ordered_pair(sK23(sK1,sK20(sK19(powerset(X0)))),sK24(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5654,c_36119]) ).
tcf(c_36918,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(powerset(X0))),sK1),relation_dom(sK1))
| element(ordered_pair(sK22(sK20(sK19(powerset(X0))),sK1),sK21(sK20(sK19(powerset(X0))),sK1)),X0)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8332,c_36119]) ).
tcf(c_36919,plain,
! [X0: $i] :
( element(ordered_pair(sK22(sK20(sK19(powerset(X0))),sK1),sK21(sK20(sK19(powerset(X0))),sK1)),X0)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(sK19(powerset(X0))),sK1)) = sK21(sK20(sK19(powerset(X0))),sK1) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5969,c_36119]) ).
tcf(c_36920,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(powerset(X0))),sK1),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(sK19(powerset(X0))),sK1),sK21(sK20(sK19(powerset(X0))),sK1)),X0)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5929,c_36119]) ).
tcf(c_36921,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK1))
| element(ordered_pair(sK21(sK1,sK20(sK19(powerset(X0)))),sK22(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_8337,c_36119]) ).
tcf(c_36922,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,sK20(sK19(powerset(X0)))),sK22(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(sK19(powerset(X0))))) = sK22(sK1,sK20(sK19(powerset(X0)))) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5964,c_36119]) ).
tcf(c_36923,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| element(ordered_pair(sK21(sK1,sK20(sK19(powerset(X0)))),sK22(sK1,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK1) )
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_5914,c_36119]) ).
tcf(c_36924,plain,
! [X0: $i] :
( element(sK5(empty_set,sK20(sK19(powerset(X0)))),X0)
| ( sK20(sK19(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8158,c_36119]) ).
tcf(c_36925,plain,
! [X0: $i] :
( element(sK13(empty_set,sK20(sK19(powerset(X0)))),X0)
| ( sK20(sK19(powerset(X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8154,c_36119]) ).
tcf(c_36926,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| element(ordered_pair(sK23(sK2,sK20(sK19(powerset(X0)))),sK24(sK2,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23755,c_36119]) ).
tcf(c_36927,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| element(ordered_pair(sK23(sK2,sK20(sK19(powerset(X0)))),sK24(sK2,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18823,c_36119]) ).
tcf(c_36928,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(sK19(powerset(X0)))),X0)
| in(sK5(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_36119]) ).
tcf(c_36929,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(sK19(powerset(X0)))),X0)
| in(sK6(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_36119]) ).
tcf(c_36930,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(sK19(powerset(X0)))),X0)
| in(sK14(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| ( sK20(sK19(powerset(X0))) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_36119]) ).
tcf(c_36931,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(sK19(powerset(X0)))),X0)
| in(sK13(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| ( sK20(sK19(powerset(X0))) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_36119]) ).
tcf(c_36932,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(sK19(powerset(X0)))),relation_dom(sK2))
| element(ordered_pair(sK21(sK2,sK20(sK19(powerset(X0)))),sK22(sK2,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23773,c_36119]) ).
tcf(c_36933,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(sK19(powerset(X0)))),relation_rng(sK2))
| element(ordered_pair(sK21(sK2,sK20(sK19(powerset(X0)))),sK22(sK2,sK20(sK19(powerset(X0))))),X0)
| ( sK20(sK19(powerset(X0))) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18841,c_36119]) ).
tcf(c_36934,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(powerset(X0))),sK2),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(sK19(powerset(X0))),sK2),sK21(sK20(sK19(powerset(X0))),sK2)),X0)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23767,c_36119]) ).
tcf(c_36935,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(powerset(X0))),sK2),relation_rng(sK2))
| element(ordered_pair(sK22(sK20(sK19(powerset(X0))),sK2),sK21(sK20(sK19(powerset(X0))),sK2)),X0)
| ( relation_inverse(sK20(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18835,c_36119]) ).
tcf(c_36936,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(powerset(X0))),sK2),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(sK19(powerset(X0))),sK2),sK24(sK20(sK19(powerset(X0))),sK2)),X0)
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_23761,c_36119]) ).
tcf(c_36937,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(powerset(X0))),sK2),relation_rng(sK2))
| element(ordered_pair(sK23(sK20(sK19(powerset(X0))),sK2),sK24(sK20(sK19(powerset(X0))),sK2)),X0)
| ( sK20(sK19(powerset(X0))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_18829,c_36119]) ).
tcf(c_36938,plain,
! [X0: $i] :
( empty(sK20(sK19(powerset(X0))))
| element(sK20(sK19(sK20(sK19(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_36111,c_36119]) ).
tcf(c_37299,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17578]) ).
tcf(c_37300,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17545]) ).
tcf(c_37301,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17544]) ).
tcf(c_37302,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17543]) ).
tcf(c_37303,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_16055]) ).
tcf(c_37304,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_16054]) ).
tcf(c_37305,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_16053]) ).
tcf(c_37306,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15952]) ).
tcf(c_37307,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15951]) ).
tcf(c_37308,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15950]) ).
tcf(c_37309,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15917]) ).
tcf(c_37310,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15916]) ).
tcf(c_37311,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15915]) ).
tcf(c_37312,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15880]) ).
tcf(c_37313,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15879]) ).
tcf(c_37314,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_15878]) ).
tcf(c_37315,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12149]) ).
tcf(c_37316,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12148]) ).
tcf(c_37317,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(sK19(powerset(X0))))) = relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11026]) ).
tcf(c_37318,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(sK19(powerset(X0))))) = relation_inverse(relation_rng(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11025]) ).
tcf(c_37319,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(sK19(powerset(X0))))) = relation_inverse(relation_dom(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11024]) ).
tcf(c_37320,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3663]) ).
tcf(c_37321,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3662]) ).
tcf(c_37322,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(sK19(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3661]) ).
tcf(c_37323,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = relation_rng(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3632]) ).
tcf(c_37324,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12146]) ).
tcf(c_37325,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = relation_inverse(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3631]) ).
tcf(c_37326,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = relation_dom(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3626]) ).
tcf(c_37327,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14780]) ).
tcf(c_37328,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14779]) ).
tcf(c_37329,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14778]) ).
tcf(c_37330,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14235]) ).
tcf(c_37331,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14234]) ).
tcf(c_37332,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14233]) ).
tcf(c_37333,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14155]) ).
tcf(c_37334,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14154]) ).
tcf(c_37335,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14153]) ).
tcf(c_37336,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14070]) ).
tcf(c_37337,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14069]) ).
tcf(c_37338,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14068]) ).
tcf(c_37339,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11811]) ).
tcf(c_37340,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11810]) ).
tcf(c_37341,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11809]) ).
tcf(c_37342,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11771]) ).
tcf(c_37343,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11770]) ).
tcf(c_37344,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11769]) ).
tcf(c_37345,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11729]) ).
tcf(c_37346,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11728]) ).
tcf(c_37347,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11727]) ).
tcf(c_37348,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11691]) ).
tcf(c_37349,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11690]) ).
tcf(c_37350,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11689]) ).
tcf(c_37351,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11660]) ).
tcf(c_37352,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11659]) ).
tcf(c_37353,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11658]) ).
tcf(c_37354,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11297]) ).
tcf(c_37355,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11296]) ).
tcf(c_37356,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_11295]) ).
tcf(c_37357,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12150]) ).
tcf(c_37358,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_9831]) ).
tcf(c_37359,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_9830]) ).
tcf(c_37360,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_9829]) ).
tcf(c_37361,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3423]) ).
tcf(c_37362,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3422]) ).
tcf(c_37363,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3421]) ).
tcf(c_37364,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3403]) ).
tcf(c_37365,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3402]) ).
tcf(c_37366,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3401]) ).
tcf(c_37367,plain,
! [X0: $i] :
( ( function_inverse(sK20(sK19(powerset(X0)))) = relation_inverse(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_957]) ).
tcf(c_37368,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3333]) ).
tcf(c_37369,plain,
! [X0: $i,X1: $i] :
( ( sK20(sK19(powerset(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_66]) ).
tcf(c_37370,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3330]) ).
tcf(c_37371,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3327]) ).
tcf(c_37373,plain,
! [X0: $i] :
( relation(sK20(sK19(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_94]) ).
tcf(c_37374,plain,
! [X0: $i] :
( function(sK20(sK19(powerset(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_85]) ).
tcf(c_37792,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(powerset(X0))))) = relation_dom(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37373,c_72]) ).
tcf(c_37793,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(powerset(X0))))) = relation_rng(sK20(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37373,c_71]) ).
tcf(c_37794,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))) = sK20(sK19(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37373,c_120]) ).
tcf(c_37845,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_36486,c_70]) ).
tcf(c_37846,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_36486,c_69]) ).
tcf(c_37848,plain,
( in(sK21(sK1,sK1),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_36486,c_106]) ).
tcf(c_37853,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK7(relation_inverse(sK1),sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_36486,c_3784]) ).
tcf(c_37854,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_37848,c_4013]) ).
tcf(c_37875,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7117,c_94,c_7117]) ).
tcf(c_37883,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK22(X0,sK1)) ),
inference(superposition,[status(thm)],[c_37875,c_70]) ).
tcf(c_37884,plain,
! [X0: $i] :
( element(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_69]) ).
tcf(c_37887,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_12701]) ).
tcf(c_37888,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_10144]) ).
tcf(c_37889,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK15(sK1,sK22(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_4468]) ).
tcf(c_37927,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17579]) ).
tcf(c_37928,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17579]) ).
tcf(c_37929,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17579]) ).
tcf(c_37930,plain,
relation_dom(relation_rng(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17579]) ).
tcf(c_37931,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17579]) ).
tcf(c_37932,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17579]) ).
tcf(c_38121,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17580]) ).
tcf(c_38122,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17580]) ).
tcf(c_38123,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17580]) ).
tcf(c_38124,plain,
relation_dom(relation_rng(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17580]) ).
tcf(c_38125,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17580]) ).
tcf(c_38126,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17580]) ).
tcf(c_38142,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17622]) ).
tcf(c_38143,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17622]) ).
tcf(c_38144,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17622]) ).
tcf(c_38145,plain,
relation_dom(relation_inverse(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17622]) ).
tcf(c_38146,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17622]) ).
tcf(c_38147,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17622]) ).
tcf(c_38163,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17623]) ).
tcf(c_38164,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17623]) ).
tcf(c_38165,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17623]) ).
tcf(c_38166,plain,
relation_dom(relation_inverse(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17623]) ).
tcf(c_38167,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17623]) ).
tcf(c_38168,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17623]) ).
tcf(c_38279,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_9067,c_94,c_9067]) ).
tcf(c_38287,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK21(X0,sK1)) ),
inference(superposition,[status(thm)],[c_38279,c_70]) ).
tcf(c_38288,plain,
! [X0: $i] :
( element(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_69]) ).
tcf(c_38291,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(X0,sK1)) = apply(sK1,sK21(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_12284]) ).
tcf(c_38292,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_4619]) ).
tcf(c_38293,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_4406]) ).
tcf(c_38316,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_9229,c_94,c_9229]) ).
tcf(c_38324,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK22(sK1,X0)) ),
inference(superposition,[status(thm)],[c_38316,c_70]) ).
tcf(c_38325,plain,
! [X0: $i] :
( element(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_69]) ).
tcf(c_38328,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK22(sK1,X0)) = apply(sK1,sK22(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_12284]) ).
tcf(c_38329,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,X0))) = sK22(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_4619]) ).
tcf(c_38330,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,X0))) = sK22(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_4406]) ).
tcf(c_38355,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10231,c_87]) ).
tcf(c_38356,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK13(sK1,empty_set)) = sK15(sK1,sK13(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10231,c_4863]) ).
tcf(c_38360,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = sK7(relation_inverse(sK1),sK13(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10231,c_4791]) ).
tcf(c_38367,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38355,c_65,c_64]) ).
tcf(c_38391,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17624]) ).
tcf(c_38392,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17624]) ).
tcf(c_38393,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17624]) ).
tcf(c_38394,plain,
relation_dom(relation_inverse(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17624]) ).
tcf(c_38395,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17624]) ).
tcf(c_38396,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17624]) ).
tcf(c_38412,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17692]) ).
tcf(c_38413,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17692]) ).
tcf(c_38414,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17692]) ).
tcf(c_38415,plain,
relation_dom(relation_inverse(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17692]) ).
tcf(c_38416,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17692]) ).
tcf(c_38417,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17692]) ).
tcf(c_38433,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17693]) ).
tcf(c_38434,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17693]) ).
tcf(c_38435,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17693]) ).
tcf(c_38436,plain,
relation_dom(relation_inverse(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17693]) ).
tcf(c_38437,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17693]) ).
tcf(c_38438,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17693]) ).
tcf(c_38454,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_17694]) ).
tcf(c_38455,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_17694]) ).
tcf(c_38456,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17694]) ).
tcf(c_38457,plain,
relation_dom(relation_inverse(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17694]) ).
tcf(c_38458,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_17694]) ).
tcf(c_38459,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_17694]) ).
tcf(c_38477,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_38367,c_70]) ).
tcf(c_38478,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38367,c_69]) ).
tcf(c_38480,plain,
( in(sK13(sK1,empty_set),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38367,c_106]) ).
tcf(c_38483,plain,
( ( relation_dom(sK2) = empty_set )
| ( relation_rng(sK1) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,empty_set),empty_set)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38367,c_104]) ).
tcf(c_38486,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = sK7(relation_inverse(sK1),sK13(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_38367,c_3784]) ).
tcf(c_38487,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_38480,c_4013]) ).
tcf(c_38498,plain,
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,empty_set),empty_set)
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_38483,c_4013]) ).
tcf(c_38505,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_14862]) ).
tcf(c_38507,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4840,c_14862]) ).
tcf(c_38508,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4863,c_14862]) ).
tcf(c_38509,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38505,c_65,c_64]) ).
tcf(c_38530,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_38509,c_70]) ).
tcf(c_38531,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_69]) ).
tcf(c_38533,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK2,ordered_pair(sK5(relation_dom(sK2),X0),X1)) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(sK5(relation_dom(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_38509,c_76]) ).
tcf(c_38534,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK2)))
| ( apply(sK2,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_38509,c_106]) ).
tcf(c_38535,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK2)))
| ( apply(sK2,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_38509,c_78]) ).
tcf(c_38536,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK2),X0) = X1 )
| ( apply(sK2,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_38509,c_197]) ).
tcf(c_38538,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(sK2,ordered_pair(X1,sK13(relation_dom(sK2),X0))) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(X1,sK13(relation_dom(sK2),X0)))) = empty_set )
| ~ relation(relation_dom(sK2))
| ~ in(sK13(relation_dom(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_38509,c_104]) ).
tcf(c_38539,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(sK2,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0) ),
inference(superposition,[status(thm)],[c_38509,c_124]) ).
tcf(c_38540,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK2))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_38509,c_129]) ).
tcf(c_38541,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_38509,c_12701]) ).
tcf(c_38542,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_38509,c_10144]) ).
tcf(c_38545,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_12622]) ).
tcf(c_38547,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(sK1,X0))) = empty_set )
| ~ in(sK13(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_38509,c_10148]) ).
tcf(c_38629,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),empty_set),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10494,c_87]) ).
tcf(c_38630,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = sK15(sK1,empty_set) )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_4863]) ).
tcf(c_38631,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ~ in(relation_dom(sK2),empty_set)
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10494,c_6246]) ).
tcf(c_38634,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = apply(relation_inverse(sK1),empty_set) )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_4791]) ).
tcf(c_38636,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_10494,c_10244]) ).
tcf(c_38638,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_10494,c_10207]) ).
tcf(c_38639,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK22(sK1,sK1) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK7(relation_inverse(sK1),sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_10494,c_10226]) ).
tcf(c_38640,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK21(sK1,sK1) = empty_set )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK7(relation_inverse(sK1),sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_10494,c_10228]) ).
tcf(c_38642,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK13(sK1,empty_set) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = sK7(relation_inverse(sK1),sK13(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_10494,c_10231]) ).
tcf(c_38694,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18055]) ).
tcf(c_38695,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18055]) ).
tcf(c_38696,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18055]) ).
tcf(c_38697,plain,
relation_dom(relation_inverse(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18055]) ).
tcf(c_38698,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18055]) ).
tcf(c_38699,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18055]) ).
tcf(c_38748,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18056]) ).
tcf(c_38749,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18056]) ).
tcf(c_38750,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18056]) ).
tcf(c_38751,plain,
relation_dom(relation_inverse(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18056]) ).
tcf(c_38752,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18056]) ).
tcf(c_38753,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18056]) ).
tcf(c_38794,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18057]) ).
tcf(c_38795,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18057]) ).
tcf(c_38796,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18057]) ).
tcf(c_38797,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18057]) ).
tcf(c_38798,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18057]) ).
tcf(c_38799,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18057]) ).
tcf(c_38829,plain,
! [X0: $i] :
( in(ordered_pair(sK13(sK1,X0),sK14(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_10593,c_87]) ).
tcf(c_38830,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(sK14(sK1,X0),sK13(sK1,X0))) ),
inference(superposition,[status(thm)],[c_10593,c_34564]) ).
tcf(c_38831,plain,
! [X0: $i] :
( element(ordered_pair(sK14(sK1,X0),sK13(sK1,X0)),sK1)
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10593,c_34565]) ).
tcf(c_38833,plain,
! [X0: $i] :
( in(ordered_pair(sK14(sK1,X0),sK13(sK1,X0)),sK1)
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10593,c_34529]) ).
tcf(c_38836,plain,
! [X0: $i] :
( in(ordered_pair(sK14(sK1,X0),sK13(sK1,X0)),sK1)
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10593,c_13488]) ).
tcf(c_38837,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,sK14(sK1,X0)) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10593,c_12807]) ).
tcf(c_38838,plain,
! [X0: $i] :
( in(ordered_pair(sK14(sK1,X0),sK13(sK1,X0)),sK1)
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10593,c_4623]) ).
tcf(c_38839,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(sK1,sK13(sK1,X0)) = sK14(sK1,X0) )
| ( apply(sK2,sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10593,c_4763]) ).
tcf(c_38871,plain,
! [X0: $i] :
( in(ordered_pair(sK13(sK1,X0),sK14(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_38829,c_4030]) ).
tcf(c_38872,plain,
! [X0: $i] :
( in(ordered_pair(sK13(sK1,X0),sK14(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38871,c_987,c_3611]) ).
tcf(c_38906,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18885]) ).
tcf(c_38907,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18885]) ).
tcf(c_38908,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18885]) ).
tcf(c_38909,plain,
relation_rng(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18885]) ).
tcf(c_38910,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18885]) ).
tcf(c_38911,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18885]) ).
tcf(c_38927,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18886]) ).
tcf(c_38928,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18886]) ).
tcf(c_38929,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18886]) ).
tcf(c_38930,plain,
relation_rng(relation_dom(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18886]) ).
tcf(c_38931,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18886]) ).
tcf(c_38932,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18886]) ).
tcf(c_38994,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18887]) ).
tcf(c_38995,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18887]) ).
tcf(c_38996,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18887]) ).
tcf(c_38997,plain,
relation_rng(relation_dom(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18887]) ).
tcf(c_38998,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18887]) ).
tcf(c_38999,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18887]) ).
tcf(c_39318,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18931]) ).
tcf(c_39319,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18931]) ).
tcf(c_39320,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18931]) ).
tcf(c_39321,plain,
relation_rng(relation_dom(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18931]) ).
tcf(c_39322,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18931]) ).
tcf(c_39323,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18931]) ).
tcf(c_39339,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18932]) ).
tcf(c_39340,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18932]) ).
tcf(c_39341,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18932]) ).
tcf(c_39342,plain,
relation_rng(relation_dom(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18932]) ).
tcf(c_39343,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18932]) ).
tcf(c_39344,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18932]) ).
tcf(c_39360,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18933]) ).
tcf(c_39361,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18933]) ).
tcf(c_39362,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18933]) ).
tcf(c_39363,plain,
relation_rng(relation_dom(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18933]) ).
tcf(c_39364,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18933]) ).
tcf(c_39365,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18933]) ).
tcf(c_39385,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_36589]) ).
tcf(c_39386,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_36589]) ).
tcf(c_39387,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_36589]) ).
tcf(c_39388,plain,
sK20(sK19(powerset(empty_set))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_36589]) ).
tcf(c_39389,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_36589]) ).
tcf(c_39390,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_36589]) ).
tcf(c_39401,plain,
( empty(sK19(powerset(empty_set)))
| ~ in(sK19(powerset(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_39388,c_3486]) ).
tcf(c_39402,plain,
( empty(sK19(powerset(empty_set)))
| in(empty_set,sK19(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_39388,c_3448]) ).
tcf(c_39403,plain,
element(empty_set,sK19(powerset(empty_set))),
inference(superposition,[status(thm)],[c_39388,c_119]) ).
tcf(c_39406,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set)) ),
inference(superposition,[status(thm)],[c_39388,c_36104]) ).
tcf(c_39572,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18984]) ).
tcf(c_39573,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18984]) ).
tcf(c_39574,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18984]) ).
tcf(c_39575,plain,
relation_rng(relation_dom(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18984]) ).
tcf(c_39576,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18984]) ).
tcf(c_39577,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18984]) ).
tcf(c_39593,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18985]) ).
tcf(c_39594,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18985]) ).
tcf(c_39595,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18985]) ).
tcf(c_39596,plain,
relation_rng(relation_dom(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18985]) ).
tcf(c_39597,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18985]) ).
tcf(c_39598,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18985]) ).
tcf(c_39668,plain,
( empty(powerset(empty_set))
| element(empty_set,powerset(empty_set))
| empty(sK19(powerset(empty_set))) ),
inference(superposition,[status(thm)],[c_39402,c_4215]) ).
tcf(c_39952,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,relation_dom(sK1)),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12316,c_107]) ).
tcf(c_39953,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12316,c_4472]) ).
tcf(c_39958,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39952,c_3821]) ).
tcf(c_39959,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39958,c_3611]) ).
tcf(c_39969,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_18986]) ).
tcf(c_39970,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_18986]) ).
tcf(c_39971,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18986]) ).
tcf(c_39972,plain,
relation_rng(relation_dom(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18986]) ).
tcf(c_39973,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_18986]) ).
tcf(c_39974,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_18986]) ).
tcf(c_39997,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19042]) ).
tcf(c_39998,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19042]) ).
tcf(c_39999,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19042]) ).
tcf(c_40000,plain,
relation_rng(relation_rng(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19042]) ).
tcf(c_40001,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19042]) ).
tcf(c_40002,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19042]) ).
tcf(c_40067,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_8164,c_8232]) ).
tcf(c_40074,plain,
( ( sK1 = empty_set )
| ~ in(relation_dom(sK2),sK22(empty_set,sK1)) ),
inference(superposition,[status(thm)],[c_40067,c_70]) ).
tcf(c_40075,plain,
( element(sK22(empty_set,sK1),relation_dom(sK2))
| ( sK1 = empty_set ) ),
inference(superposition,[status(thm)],[c_40067,c_69]) ).
tcf(c_40078,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40067,c_12701]) ).
tcf(c_40079,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40067,c_10144]) ).
tcf(c_40080,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_40067,c_4468]) ).
tcf(c_40639,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12330,c_107]) ).
tcf(c_40640,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12330,c_4472]) ).
tcf(c_40645,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40639,c_3821]) ).
tcf(c_40646,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40645,c_3611]) ).
tcf(c_40803,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12332,c_107]) ).
tcf(c_40804,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12332,c_4472]) ).
tcf(c_40809,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40803,c_3821]) ).
tcf(c_40810,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40809,c_3611]) ).
tcf(c_40821,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12139]) ).
tcf(c_40822,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12139]) ).
tcf(c_40823,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12139]) ).
tcf(c_40824,plain,
relation_rng(relation_inverse(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12139]) ).
tcf(c_40825,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12139]) ).
tcf(c_40826,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12139]) ).
tcf(c_41062,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK14(sK1,empty_set),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12336,c_107]) ).
tcf(c_41063,plain,
( in(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12336,c_4472]) ).
tcf(c_41067,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41062,c_3821]) ).
tcf(c_41068,plain,
( in(ordered_pair(apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41067,c_3611]) ).
tcf(c_41076,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19043]) ).
tcf(c_41077,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19043]) ).
tcf(c_41078,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19043]) ).
tcf(c_41079,plain,
relation_rng(relation_rng(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19043]) ).
tcf(c_41080,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19043]) ).
tcf(c_41081,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19043]) ).
tcf(c_41097,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19044]) ).
tcf(c_41098,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19044]) ).
tcf(c_41099,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19044]) ).
tcf(c_41100,plain,
relation_rng(relation_rng(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19044]) ).
tcf(c_41101,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19044]) ).
tcf(c_41102,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19044]) ).
tcf(c_41120,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12140]) ).
tcf(c_41121,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12140]) ).
tcf(c_41122,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12140]) ).
tcf(c_41123,plain,
relation_rng(relation_rng(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12140]) ).
tcf(c_41124,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12140]) ).
tcf(c_41125,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12140]) ).
tcf(c_41141,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12141]) ).
tcf(c_41142,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12141]) ).
tcf(c_41143,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12141]) ).
tcf(c_41144,plain,
relation_rng(relation_dom(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12141]) ).
tcf(c_41145,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12141]) ).
tcf(c_41146,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12141]) ).
tcf(c_41162,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12142]) ).
tcf(c_41163,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12142]) ).
tcf(c_41164,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12142]) ).
tcf(c_41165,plain,
relation_dom(relation_inverse(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12142]) ).
tcf(c_41166,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12142]) ).
tcf(c_41167,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12142]) ).
tcf(c_41183,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12143]) ).
tcf(c_41184,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12143]) ).
tcf(c_41185,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12143]) ).
tcf(c_41186,plain,
relation_dom(relation_rng(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12143]) ).
tcf(c_41187,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12143]) ).
tcf(c_41188,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12143]) ).
tcf(c_41599,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19621]) ).
tcf(c_41600,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19621]) ).
tcf(c_41601,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19621]) ).
tcf(c_41602,plain,
relation_rng(relation_rng(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19621]) ).
tcf(c_41603,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19621]) ).
tcf(c_41604,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19621]) ).
tcf(c_41620,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19622]) ).
tcf(c_41621,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19622]) ).
tcf(c_41622,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19622]) ).
tcf(c_41623,plain,
relation_rng(relation_rng(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19622]) ).
tcf(c_41624,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19622]) ).
tcf(c_41625,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19622]) ).
tcf(c_41815,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12144]) ).
tcf(c_41816,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12144]) ).
tcf(c_41817,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12144]) ).
tcf(c_41818,plain,
relation_dom(relation_dom(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_12144]) ).
tcf(c_41819,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12144]) ).
tcf(c_41820,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12144]) ).
tcf(c_41836,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14077]) ).
tcf(c_41837,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14077]) ).
tcf(c_41838,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14077]) ).
tcf(c_41839,plain,
relation_inverse(relation_dom(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14077]) ).
tcf(c_41840,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14077]) ).
tcf(c_41841,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14077]) ).
tcf(c_41857,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14162]) ).
tcf(c_41858,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14162]) ).
tcf(c_41859,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14162]) ).
tcf(c_41860,plain,
relation_inverse(relation_rng(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14162]) ).
tcf(c_41861,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14162]) ).
tcf(c_41862,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14162]) ).
tcf(c_41878,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14242]) ).
tcf(c_41879,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14242]) ).
tcf(c_41880,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14242]) ).
tcf(c_41881,plain,
relation_inverse(relation_inverse(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14242]) ).
tcf(c_41882,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14242]) ).
tcf(c_41883,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14242]) ).
tcf(c_41918,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12634,c_87]) ).
tcf(c_41923,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = apply(sK1,empty_set) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12634,c_12764]) ).
tcf(c_41924,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12634,c_9713]) ).
tcf(c_41925,plain,
( in(ordered_pair(empty_set,sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12634,c_13488]) ).
tcf(c_41926,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = apply(sK1,empty_set) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12634,c_12807]) ).
tcf(c_41927,plain,
( in(ordered_pair(empty_set,sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12634,c_4623]) ).
tcf(c_41928,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12634,c_4763]) ).
tcf(c_41953,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_41918,c_4030]) ).
tcf(c_41954,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41953,c_987,c_3611]) ).
tcf(c_41983,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_19623]) ).
tcf(c_41984,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_19623]) ).
tcf(c_41985,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19623]) ).
tcf(c_41986,plain,
relation_rng(relation_rng(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19623]) ).
tcf(c_41987,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_19623]) ).
tcf(c_41988,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_19623]) ).
tcf(c_42004,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20565]) ).
tcf(c_42005,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20565]) ).
tcf(c_42006,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20565]) ).
tcf(c_42007,plain,
relation_rng(relation_rng(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20565]) ).
tcf(c_42008,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20565]) ).
tcf(c_42009,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20565]) ).
tcf(c_42025,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20566]) ).
tcf(c_42026,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20566]) ).
tcf(c_42027,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20566]) ).
tcf(c_42028,plain,
relation_rng(relation_rng(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20566]) ).
tcf(c_42029,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20566]) ).
tcf(c_42030,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20566]) ).
tcf(c_42046,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20567]) ).
tcf(c_42047,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20567]) ).
tcf(c_42048,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20567]) ).
tcf(c_42049,plain,
relation_rng(relation_rng(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20567]) ).
tcf(c_42050,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20567]) ).
tcf(c_42051,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20567]) ).
tcf(c_42067,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_14787]) ).
tcf(c_42068,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_14787]) ).
tcf(c_42069,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_14787]) ).
tcf(c_42070,plain,
sK20(powerset(sK20(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_14787]) ).
tcf(c_42071,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_14787]) ).
tcf(c_42072,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_14787]) ).
tcf(c_42205,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2))
| ~ in(sK2,ordered_pair(X0,sK15(relation_inverse(sK2),X0))) ),
inference(superposition,[status(thm)],[c_31806,c_70]) ).
tcf(c_42206,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK15(relation_inverse(sK2),X0)),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31806,c_69]) ).
tcf(c_42208,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0)
| ~ in(sK5(sK2,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31806,c_76]) ).
tcf(c_42209,plain,
! [X0: $i] :
( in(sK15(relation_inverse(sK2),X0),relation_rng(sK2))
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31806,c_106]) ).
tcf(c_42211,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31806,c_197]) ).
tcf(c_42213,plain,
! [X0: $i] :
( in(sK15(relation_inverse(sK2),X0),relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31806,c_18433]) ).
tcf(c_42224,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42211,c_62,c_61]) ).
tcf(c_42228,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0)
| ~ in(sK5(sK2,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42208,c_61]) ).
tcf(c_42250,plain,
! [X0: $i] :
( in(ordered_pair(sK6(sK1,X0),sK5(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_12637,c_87]) ).
tcf(c_42251,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(sK5(sK1,X0),sK6(sK1,X0))) ),
inference(superposition,[status(thm)],[c_12637,c_34564]) ).
tcf(c_42252,plain,
! [X0: $i] :
( element(ordered_pair(sK5(sK1,X0),sK6(sK1,X0)),sK1)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12637,c_34565]) ).
tcf(c_42254,plain,
! [X0: $i] :
( in(ordered_pair(sK5(sK1,X0),sK6(sK1,X0)),sK1)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12637,c_34529]) ).
tcf(c_42255,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = sK6(sK1,X0) )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12637,c_12764]) ).
tcf(c_42256,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( sK15(sK1,sK6(sK1,X0)) = sK5(sK1,X0) )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12637,c_9713]) ).
tcf(c_42257,plain,
! [X0: $i] :
( in(ordered_pair(sK5(sK1,X0),sK6(sK1,X0)),sK1)
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK6(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12637,c_13488]) ).
tcf(c_42258,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12637,c_12807]) ).
tcf(c_42259,plain,
! [X0: $i] :
( in(ordered_pair(sK5(sK1,X0),sK6(sK1,X0)),sK1)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK6(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12637,c_4623]) ).
tcf(c_42260,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( sK15(sK1,sK6(sK1,X0)) = sK5(sK1,X0) )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12637,c_4763]) ).
tcf(c_42298,plain,
! [X0: $i] :
( in(ordered_pair(sK6(sK1,X0),sK5(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_42250,c_4030]) ).
tcf(c_42299,plain,
! [X0: $i] :
( in(ordered_pair(sK6(sK1,X0),sK5(sK1,X0)),relation_inverse(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK6(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42298,c_987,c_3611]) ).
tcf(c_42338,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20731]) ).
tcf(c_42339,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20731]) ).
tcf(c_42340,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20731]) ).
tcf(c_42341,plain,
relation_rng(relation_inverse(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20731]) ).
tcf(c_42342,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20731]) ).
tcf(c_42343,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20731]) ).
tcf(c_42359,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20732]) ).
tcf(c_42360,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20732]) ).
tcf(c_42361,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20732]) ).
tcf(c_42362,plain,
relation_rng(relation_inverse(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20732]) ).
tcf(c_42363,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20732]) ).
tcf(c_42364,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20732]) ).
tcf(c_42380,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20733]) ).
tcf(c_42381,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20733]) ).
tcf(c_42382,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20733]) ).
tcf(c_42383,plain,
relation_rng(relation_inverse(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20733]) ).
tcf(c_42384,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20733]) ).
tcf(c_42385,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20733]) ).
tcf(c_42401,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20788]) ).
tcf(c_42402,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20788]) ).
tcf(c_42403,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20788]) ).
tcf(c_42404,plain,
relation_rng(relation_inverse(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20788]) ).
tcf(c_42405,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20788]) ).
tcf(c_42406,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20788]) ).
tcf(c_42424,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_89,c_42224]) ).
tcf(c_42425,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_42224]) ).
tcf(c_42426,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),ordered_pair(X0,sK7(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(X0,sK7(relation_dom(sK2),X0))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_42224]) ).
tcf(c_42427,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),ordered_pair(X0,apply(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(X0,apply(relation_dom(sK2),X0))) )
| ~ function(relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_42224]) ).
tcf(c_42428,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_42224]) ).
tcf(c_42429,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),ordered_pair(sK15(relation_dom(sK2),X0),X0)) = apply(sK2,ordered_pair(sK15(relation_dom(sK2),X0),X0)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_42224]) ).
tcf(c_42430,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_42224]) ).
tcf(c_42431,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_42224]) ).
tcf(c_42432,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_42224]) ).
tcf(c_42433,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_42224]) ).
tcf(c_42434,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK2),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_42224]) ).
tcf(c_42435,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_38509,c_42224]) ).
tcf(c_42436,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4546,c_42224]) ).
tcf(c_42437,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),sK7(sK1,X0)) = apply(sK2,sK7(sK1,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_42224]) ).
tcf(c_42438,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),apply(sK1,X0)) = apply(sK2,apply(sK1,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_42224]) ).
tcf(c_42440,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5275,c_42224]) ).
tcf(c_42441,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8548,c_42224]) ).
tcf(c_42442,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6286,c_42224]) ).
tcf(c_42443,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8302,c_42224]) ).
tcf(c_42444,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_42224]) ).
tcf(c_42445,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5141,c_42224]) ).
tcf(c_42446,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK6(sK1,X0)) = apply(sK2,sK6(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6280,c_42224]) ).
tcf(c_42447,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK6(sK1,X0)) = apply(sK2,sK6(sK1,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6281,c_42224]) ).
tcf(c_42448,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK6(sK1,X0)) = apply(sK2,sK6(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_42224]) ).
tcf(c_42454,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK13(sK1,X0)) = apply(sK2,sK13(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6330,c_42224]) ).
tcf(c_42455,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK13(sK1,X0)) = apply(sK2,sK13(sK1,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6331,c_42224]) ).
tcf(c_42456,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK13(sK1,X0)) = apply(sK2,sK13(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_42224]) ).
tcf(c_42457,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_42224]) ).
tcf(c_42458,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_42224]) ).
tcf(c_42459,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_42224]) ).
tcf(c_42460,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK2),sK24(X0,sK1)) = apply(sK2,sK24(X0,sK1)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32648,c_42224]) ).
tcf(c_42461,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_42224]) ).
tcf(c_42462,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_42224]) ).
tcf(c_42463,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_42224]) ).
tcf(c_42464,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,X0)) = apply(sK2,sK24(sK1,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32618,c_42224]) ).
tcf(c_42465,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_42224]) ).
tcf(c_42466,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_42224]) ).
tcf(c_42467,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_42224]) ).
tcf(c_42468,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(X0,sK1)) = apply(sK2,sK22(X0,sK1)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_37875,c_42224]) ).
tcf(c_42469,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_42224]) ).
tcf(c_42470,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_42224]) ).
tcf(c_42471,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_42224]) ).
tcf(c_42472,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK21(sK1,X0)) = apply(sK2,sK21(sK1,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_36354,c_42224]) ).
tcf(c_42473,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8310,c_42224]) ).
tcf(c_42474,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_7149,c_42224]) ).
tcf(c_42475,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8306,c_42224]) ).
tcf(c_42476,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6706,c_42224]) ).
tcf(c_42477,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6686,c_42224]) ).
tcf(c_42478,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK2),sK5(empty_set,relation_dom(sK2))) = apply(sK2,sK5(empty_set,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8158,c_42224]) ).
tcf(c_42479,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK2),sK13(empty_set,relation_dom(sK2))) = apply(sK2,sK13(empty_set,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8154,c_42224]) ).
tcf(c_42481,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK2),sK13(sK1,empty_set)) = apply(sK2,sK13(sK1,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8131,c_42224]) ).
tcf(c_42486,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_42224]) ).
tcf(c_42487,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_42224]) ).
tcf(c_42490,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK2,relation_dom(sK2))) = apply(sK2,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_42224]) ).
tcf(c_42491,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK2,relation_dom(sK2))) = apply(sK2,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_42224]) ).
tcf(c_42492,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_42224]) ).
tcf(c_42493,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK2),ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) = apply(sK2,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_42224]) ).
tcf(c_42494,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_42224]) ).
tcf(c_42495,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) = apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_42224]) ).
tcf(c_42496,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_42224]) ).
tcf(c_42497,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK2),ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) = apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_42224]) ).
tcf(c_42498,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_42224]) ).
tcf(c_42499,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_42224]) ).
tcf(c_42500,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK2,sK1)) = apply(sK2,sK22(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_42224]) ).
tcf(c_42501,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_42224]) ).
tcf(c_42502,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK5(sK2,X0)) = apply(sK2,sK5(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_42224]) ).
tcf(c_42503,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK14(sK2,X0)) = apply(sK2,sK14(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_42224]) ).
tcf(c_42504,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),sK15(sK2,X0)) = apply(sK2,sK15(sK2,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_42224]) ).
tcf(c_42505,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_42224]) ).
tcf(c_42506,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_42224]) ).
tcf(c_42507,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_42224]) ).
tcf(c_42508,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_42224]) ).
tcf(c_42509,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( sK15(relation_inverse(sK2),sK21(sK2,sK2)) = apply(sK2,sK21(sK2,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_42224]) ).
tcf(c_42510,plain,
( ( relation_rng(sK2) = empty_set )
| ( sK15(relation_inverse(sK2),sK14(sK2,empty_set)) = apply(sK2,sK14(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_42224]) ).
tcf(c_42511,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK2),sK5(sK2,empty_set)) = apply(sK2,sK5(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_42224]) ).
tcf(c_42512,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_dom(X0))) = apply(sK2,sK6(sK1,relation_dom(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_29857,c_42224]) ).
tcf(c_42513,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_dom(X0))) = apply(sK2,sK13(sK1,relation_dom(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_29868,c_42224]) ).
tcf(c_42514,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_rng(X0))) = apply(sK2,sK6(sK1,relation_rng(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_30437,c_42224]) ).
tcf(c_42515,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_rng(X0))) = apply(sK2,sK13(sK1,relation_rng(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_30446,c_42224]) ).
tcf(c_42517,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK2),sK20(sK19(relation_dom(sK2)))) = apply(sK2,sK20(sK19(relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_36111,c_42224]) ).
tcf(c_42596,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42424,c_62,c_61]) ).
tcf(c_43044,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42596]) ).
tcf(c_43046,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK2),X0) = apply(sK2,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43044,c_61]) ).
tcf(c_43056,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),relation_inverse(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_43046,c_107]) ).
tcf(c_43057,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK2,X0)),sK2)
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_43046,c_31806]) ).
tcf(c_43062,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),relation_inverse(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_43056,c_3845]) ).
tcf(c_43077,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(sK2,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_89,c_42228]) ).
tcf(c_43078,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(sK2,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK2,X0))) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_38509,c_42228]) ).
tcf(c_43079,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK5(sK2,X0)) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_4546,c_42228]) ).
tcf(c_43083,plain,
( ( relation_dom(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_24805,c_42228]) ).
tcf(c_43088,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(sK2,X0)) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43077,c_62,c_61]) ).
tcf(c_43108,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_dom(X0))) = empty_set )
| ( apply(X0,sK5(sK2,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_89,c_43088]) ).
tcf(c_43111,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_rng(sK12))) = empty_set )
| ( apply(relation_inverse(sK12),sK5(sK2,relation_rng(sK12))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5420,c_43088]) ).
tcf(c_43112,plain,
! [X0: $i] :
( in(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(sK2,X0)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_43088]) ).
tcf(c_43113,plain,
! [X0: $i] :
( in(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(sK2,X0)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_43088]) ).
tcf(c_43142,plain,
! [X0: $i] :
( ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2))
| ~ in(sK2,ordered_pair(sK7(relation_inverse(sK2),X0),X0)) ),
inference(superposition,[status(thm)],[c_31810,c_70]) ).
tcf(c_43143,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK2),X0),X0),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_31810,c_69]) ).
tcf(c_43146,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK2),X0),relation_dom(sK2))
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_31810,c_78]) ).
tcf(c_43147,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),X0)) = X0 )
| ~ function(sK2)
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_31810,c_197]) ).
tcf(c_43148,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,X0),X0)
| ~ in(sK13(sK2,X0),relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_31810,c_104]) ).
tcf(c_43149,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK2),X0),relation_dom(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_31810,c_18437]) ).
tcf(c_43161,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),X0)) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43147,c_62,c_61]) ).
tcf(c_43165,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,X0),X0)
| ~ in(sK13(sK2,X0),relation_rng(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43148,c_61]) ).
tcf(c_43181,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK2),X0),X0)
| ( relation_dom(relation_rng(sK2)) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK5(relation_rng(sK2),X0),sK6(relation_rng(sK2),X0)))) = ordered_pair(sK5(relation_rng(sK2),X0),sK6(relation_rng(sK2),X0)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_43161]) ).
tcf(c_43182,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(X0,sK7(relation_rng(sK2),X0)))) = ordered_pair(X0,sK7(relation_rng(sK2),X0)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_43161]) ).
tcf(c_43183,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(X0,apply(relation_rng(sK2),X0)))) = ordered_pair(X0,apply(relation_rng(sK2),X0)) )
| ~ function(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_dom(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_87,c_43161]) ).
tcf(c_43184,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK2),X0),X0)
| ( relation_rng(relation_rng(sK2)) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK14(relation_rng(sK2),X0),sK13(relation_rng(sK2),X0)))) = ordered_pair(sK14(relation_rng(sK2),X0),sK13(relation_rng(sK2),X0)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_43161]) ).
tcf(c_43185,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK15(relation_rng(sK2),X0),X0))) = ordered_pair(sK15(relation_rng(sK2),X0),X0) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(X0,relation_rng(relation_rng(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_43161]) ).
tcf(c_43186,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0)
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),X0),sK21(relation_rng(sK2),X0)))) = ordered_pair(sK22(relation_rng(sK2),X0),sK21(relation_rng(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_43161]) ).
tcf(c_43187,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK2)),sK21(X0,relation_rng(sK2))),X0)
| ( relation_inverse(X0) = relation_rng(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(X0,relation_rng(sK2)),sK22(X0,relation_rng(sK2))))) = ordered_pair(sK21(X0,relation_rng(sK2)),sK22(X0,relation_rng(sK2))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_43161]) ).
tcf(c_43188,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))))) = ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_43161]) ).
tcf(c_43189,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)))) = ordered_pair(sK23(relation_rng(sK2),X0),sK24(relation_rng(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_43161]) ).
tcf(c_43190,plain,
( empty(relation_rng(sK2))
| ( apply(sK2,sK7(relation_inverse(sK2),sK20(relation_rng(sK2)))) = sK20(relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3448,c_43161]) ).
tcf(c_43191,plain,
( element(sK5(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,relation_rng(sK2)))) = sK5(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8548,c_43161]) ).
tcf(c_43192,plain,
( element(sK6(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,relation_rng(sK2)))) = sK5(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6286,c_43161]) ).
tcf(c_43193,plain,
( in(sK5(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,relation_rng(sK2)))) = sK5(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8302,c_43161]) ).
tcf(c_43194,plain,
( in(sK6(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,relation_rng(sK2)))) = sK5(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5335,c_43161]) ).
tcf(c_43195,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK2))) = sK5(sK1,relation_rng(sK2)) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,relation_rng(sK2)))) = sK5(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5141,c_43161]) ).
tcf(c_43196,plain,
( element(sK14(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK1,relation_rng(sK2)))) = sK13(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8430,c_43161]) ).
tcf(c_43197,plain,
( element(sK13(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK1,relation_rng(sK2)))) = sK13(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6336,c_43161]) ).
tcf(c_43198,plain,
( in(sK14(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK1,relation_rng(sK2)))) = sK13(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8298,c_43161]) ).
tcf(c_43199,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = sK14(sK1,relation_rng(sK2)) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK1,relation_rng(sK2)))) = sK13(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5563,c_43161]) ).
tcf(c_43200,plain,
( in(sK13(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK1,relation_rng(sK2)))) = sK13(sK1,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_5542,c_43161]) ).
tcf(c_43201,plain,
( in(sK23(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)))) = ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_43161]) ).
tcf(c_43202,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK2),sK1)) = sK23(relation_rng(sK2),sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)))) = ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_43161]) ).
tcf(c_43203,plain,
( in(sK24(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)))) = ordered_pair(sK23(relation_rng(sK2),sK1),sK24(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_43161]) ).
tcf(c_43204,plain,
( in(sK23(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))))) = ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_43161]) ).
tcf(c_43205,plain,
( ( relation_rng(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK2))) = sK23(sK1,relation_rng(sK2)) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))))) = ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_43161]) ).
tcf(c_43206,plain,
( in(sK24(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))))) = ordered_pair(sK23(sK1,relation_rng(sK2)),sK24(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_43161]) ).
tcf(c_43207,plain,
( in(sK21(relation_rng(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)))) = ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_43161]) ).
tcf(c_43208,plain,
( ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK2),sK1)) = sK21(relation_rng(sK2),sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)))) = ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_43161]) ).
tcf(c_43209,plain,
( in(sK22(relation_rng(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)))) = ordered_pair(sK22(relation_rng(sK2),sK1),sK21(relation_rng(sK2),sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_43161]) ).
tcf(c_43210,plain,
( in(sK22(sK1,relation_rng(sK2)),relation_dom(sK1))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))))) = ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_43161]) ).
tcf(c_43211,plain,
( ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK2))) = sK22(sK1,relation_rng(sK2)) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))))) = ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_43161]) ).
tcf(c_43212,plain,
( in(sK21(sK1,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))))) = ordered_pair(sK21(sK1,relation_rng(sK2)),sK22(sK1,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_43161]) ).
tcf(c_43213,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(empty_set,relation_rng(sK2)))) = sK5(empty_set,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8158,c_43161]) ).
tcf(c_43214,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(empty_set,relation_rng(sK2)))) = sK13(empty_set,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8154,c_43161]) ).
tcf(c_43215,plain,
( in(sK23(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(sK2,relation_rng(sK2)),sK24(sK2,relation_rng(sK2))))) = ordered_pair(sK23(sK2,relation_rng(sK2)),sK24(sK2,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_43161]) ).
tcf(c_43216,plain,
( in(sK24(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(sK2,relation_rng(sK2)),sK24(sK2,relation_rng(sK2))))) = ordered_pair(sK23(sK2,relation_rng(sK2)),sK24(sK2,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_43161]) ).
tcf(c_43217,plain,
( in(sK5(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK2,relation_rng(sK2)))) = sK5(sK2,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_43161]) ).
tcf(c_43218,plain,
( in(sK6(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK2,relation_rng(sK2)))) = sK5(sK2,relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_43161]) ).
tcf(c_43219,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK6(sK2,X0))) = sK6(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_43161]) ).
tcf(c_43220,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),sK7(sK2,X0))) = sK7(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18720,c_43161]) ).
tcf(c_43221,plain,
! [X0: $i] :
( ( apply(sK2,sK7(relation_inverse(sK2),apply(sK2,X0))) = apply(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18734,c_43161]) ).
tcf(c_43224,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK2,X0))) = sK13(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_43161]) ).
tcf(c_43225,plain,
( in(sK22(sK2,relation_rng(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(sK2,relation_rng(sK2)),sK22(sK2,relation_rng(sK2))))) = ordered_pair(sK21(sK2,relation_rng(sK2)),sK22(sK2,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_43161]) ).
tcf(c_43226,plain,
( in(sK21(sK2,relation_rng(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_inverse(sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK21(sK2,relation_rng(sK2)),sK22(sK2,relation_rng(sK2))))) = ordered_pair(sK21(sK2,relation_rng(sK2)),sK22(sK2,relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_43161]) ).
tcf(c_43227,plain,
( in(sK21(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),sK2),sK21(relation_rng(sK2),sK2)))) = ordered_pair(sK22(relation_rng(sK2),sK2),sK21(relation_rng(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_43161]) ).
tcf(c_43228,plain,
( in(sK22(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK2)) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),sK2),sK21(relation_rng(sK2),sK2)))) = ordered_pair(sK22(relation_rng(sK2),sK2),sK21(relation_rng(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_43161]) ).
tcf(c_43229,plain,
( in(sK23(relation_rng(sK2),sK2),relation_dom(sK2))
| ( relation_rng(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),sK2),sK24(relation_rng(sK2),sK2)))) = ordered_pair(sK23(relation_rng(sK2),sK2),sK24(relation_rng(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_43161]) ).
tcf(c_43230,plain,
( in(sK24(relation_rng(sK2),sK2),relation_rng(sK2))
| ( relation_rng(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),ordered_pair(sK23(relation_rng(sK2),sK2),sK24(relation_rng(sK2),sK2)))) = ordered_pair(sK23(relation_rng(sK2),sK2),sK24(relation_rng(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_43161]) ).
tcf(c_43231,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18803,c_43161]) ).
tcf(c_43232,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18763,c_43161]) ).
tcf(c_43233,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18758,c_43161]) ).
tcf(c_43234,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18798,c_43161]) ).
tcf(c_43235,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18753,c_43161]) ).
tcf(c_43236,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18748,c_43161]) ).
tcf(c_43237,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK21(sK2,sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK1))) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18818,c_43161]) ).
tcf(c_43238,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK1))) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18793,c_43161]) ).
tcf(c_43239,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK22(sK1,sK2) )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,sK2))) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18813,c_43161]) ).
tcf(c_43240,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,sK2))) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18783,c_43161]) ).
tcf(c_43241,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK2,empty_set))) = sK13(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19961,c_43161]) ).
tcf(c_43242,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK6(sK2,empty_set))) = sK6(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20120,c_43161]) ).
tcf(c_43243,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK2,sK2))) = sK22(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23719,c_43161]) ).
tcf(c_43244,plain,
( in(sK21(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK2))) = sK21(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23724,c_43161]) ).
tcf(c_43245,plain,
( in(sK22(sK2,sK2),relation_rng(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK2))) = sK21(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_21834,c_43161]) ).
tcf(c_43246,plain,
( empty(relation_rng(sK2))
| ( apply(sK2,sK7(relation_inverse(sK2),sK20(sK19(relation_rng(sK2))))) = sK20(sK19(relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_36111,c_43161]) ).
tcf(c_43883,plain,
( ( relation_rng(sK2) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_19961,c_43165]) ).
tcf(c_43920,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20789]) ).
tcf(c_43921,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20789]) ).
tcf(c_43922,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20789]) ).
tcf(c_43923,plain,
relation_rng(relation_inverse(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20789]) ).
tcf(c_43924,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20789]) ).
tcf(c_43925,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20789]) ).
tcf(c_43941,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_20790]) ).
tcf(c_43942,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_20790]) ).
tcf(c_43943,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20790]) ).
tcf(c_43944,plain,
relation_rng(relation_inverse(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20790]) ).
tcf(c_43945,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_20790]) ).
tcf(c_43946,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_20790]) ).
tcf(c_43962,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_21077]) ).
tcf(c_43963,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_21077]) ).
tcf(c_43964,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_21077]) ).
tcf(c_43965,plain,
relation_rng(relation_inverse(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_21077]) ).
tcf(c_43966,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_21077]) ).
tcf(c_43967,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_21077]) ).
tcf(c_43983,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_21078]) ).
tcf(c_43984,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_21078]) ).
tcf(c_43985,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_21078]) ).
tcf(c_43986,plain,
relation_rng(relation_inverse(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_21078]) ).
tcf(c_43987,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_21078]) ).
tcf(c_43988,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_21078]) ).
tcf(c_44027,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK1),sK5(sK1,relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_32144,c_70]) ).
tcf(c_44031,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_rng(sK9))) = apply(sK1,sK5(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_12284]) ).
tcf(c_44032,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK9)))) = sK5(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_4619]) ).
tcf(c_44033,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK9)))) = sK5(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_4406]) ).
tcf(c_44034,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ in(sK5(sK1,relation_rng(sK9)),relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_12287]) ).
tcf(c_44056,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK2),sK6(sK1,relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_32145,c_70]) ).
tcf(c_44060,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_rng(sK9))) = apply(sK2,sK6(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32145,c_42224]) ).
tcf(c_44061,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK9)))) = sK6(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_12701]) ).
tcf(c_44062,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_rng(sK9)))) = sK6(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_10144]) ).
tcf(c_44063,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK9))) = sK15(sK1,sK6(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_4468]) ).
tcf(c_49656,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK1),sK14(sK1,relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_32147,c_70]) ).
tcf(c_49660,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_rng(sK9))) = apply(sK1,sK14(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_12284]) ).
tcf(c_49661,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK9)))) = sK14(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_4619]) ).
tcf(c_49662,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK9)))) = sK14(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_4406]) ).
tcf(c_49691,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK2),sK13(sK1,relation_rng(sK9))) ),
inference(superposition,[status(thm)],[c_32149,c_70]) ).
tcf(c_49695,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_rng(sK9))) = apply(sK2,sK13(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32149,c_42224]) ).
tcf(c_49696,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK9)))) = sK13(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_12701]) ).
tcf(c_49697,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_rng(sK9)))) = sK13(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_10144]) ).
tcf(c_49698,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK9))) = sK15(sK1,sK13(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_4468]) ).
tcf(c_49699,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK9))
| ~ in(sK13(sK1,relation_rng(sK9)),relation_rng(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_10148]) ).
tcf(c_49725,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK1),sK5(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_32763,c_70]) ).
tcf(c_49729,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_rng(sK12))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_12284]) ).
tcf(c_49730,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_4619]) ).
tcf(c_49731,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_4406]) ).
tcf(c_49732,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_12287]) ).
tcf(c_49831,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK2),sK6(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_32764,c_70]) ).
tcf(c_49835,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_rng(sK12))) = apply(sK2,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32764,c_42224]) ).
tcf(c_49836,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_12701]) ).
tcf(c_49837,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_10144]) ).
tcf(c_49838,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_4468]) ).
tcf(c_49861,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK1),sK14(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_32768,c_70]) ).
tcf(c_49865,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_rng(sK12))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_12284]) ).
tcf(c_49866,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_4619]) ).
tcf(c_49867,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_4406]) ).
tcf(c_49886,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK2),sK13(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_32770,c_70]) ).
tcf(c_49890,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_rng(sK12))) = apply(sK2,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32770,c_42224]) ).
tcf(c_49891,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_12701]) ).
tcf(c_49892,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_10144]) ).
tcf(c_49893,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_4468]) ).
tcf(c_49894,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_inverse(sK12))
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_10148]) ).
tcf(c_49920,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_9713,c_12770]) ).
tcf(c_49921,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_4763,c_12770]) ).
tcf(c_49922,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = apply(sK1,empty_set) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_12634,c_12770]) ).
tcf(c_49926,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_87]) ).
tcf(c_49928,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(relation_dom(sK2),sK5(sK1,relation_dom(sK2)))
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_6246]) ).
tcf(c_49929,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_6247]) ).
tcf(c_49930,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_5332]) ).
tcf(c_49959,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49926,c_65,c_64]) ).
tcf(c_49982,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_21079]) ).
tcf(c_49983,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_21079]) ).
tcf(c_49984,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_21079]) ).
tcf(c_49985,plain,
relation_rng(relation_inverse(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_21079]) ).
tcf(c_49986,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_21079]) ).
tcf(c_49987,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_21079]) ).
tcf(c_50003,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_22303]) ).
tcf(c_50004,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_22303]) ).
tcf(c_50005,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_22303]) ).
tcf(c_50006,plain,
relation_inverse(relation_dom(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_22303]) ).
tcf(c_50007,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_22303]) ).
tcf(c_50008,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_22303]) ).
tcf(c_50043,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_22304]) ).
tcf(c_50044,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_22304]) ).
tcf(c_50045,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_22304]) ).
tcf(c_50046,plain,
relation_inverse(relation_dom(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_22304]) ).
tcf(c_50047,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_22304]) ).
tcf(c_50048,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_22304]) ).
tcf(c_50106,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_22305]) ).
tcf(c_50107,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_22305]) ).
tcf(c_50108,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_22305]) ).
tcf(c_50109,plain,
relation_inverse(relation_dom(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_22305]) ).
tcf(c_50110,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_22305]) ).
tcf(c_50111,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_22305]) ).
tcf(c_50131,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_49959]) ).
tcf(c_50132,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_49959]) ).
tcf(c_50133,plain,
( in(ordered_pair(empty_set,sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12634,c_49959]) ).
tcf(c_50134,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_49959,c_70]) ).
tcf(c_50135,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_49959,c_69]) ).
tcf(c_50137,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_49959,c_106]) ).
tcf(c_50143,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_50137,c_4013]) ).
tcf(c_50282,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK1),sK5(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_32993,c_70]) ).
tcf(c_50286,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_dom(sK12))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_12284]) ).
tcf(c_50287,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_4619]) ).
tcf(c_50288,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_4406]) ).
tcf(c_50289,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(sK5(sK1,relation_dom(sK12)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_12287]) ).
tcf(c_50311,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK2),sK6(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_32994,c_70]) ).
tcf(c_50315,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_dom(sK12))) = apply(sK2,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32994,c_42224]) ).
tcf(c_50316,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_12701]) ).
tcf(c_50317,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_10144]) ).
tcf(c_50318,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_4468]) ).
tcf(c_50341,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK1),sK14(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_32997,c_70]) ).
tcf(c_50345,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_dom(sK12))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_12284]) ).
tcf(c_50346,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_4619]) ).
tcf(c_50347,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_4406]) ).
tcf(c_50366,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(relation_dom(sK2),sK13(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_32999,c_70]) ).
tcf(c_50370,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_dom(sK12))) = apply(sK2,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32999,c_42224]) ).
tcf(c_50371,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_12701]) ).
tcf(c_50372,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_10144]) ).
tcf(c_50373,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_4468]) ).
tcf(c_50374,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_inverse(sK12))
| ~ in(sK13(sK1,relation_dom(sK12)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_10148]) ).
tcf(c_50531,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK1),sK5(sK1,relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_33532,c_70]) ).
tcf(c_50535,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_dom(sK9))) = apply(sK1,sK5(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_12284]) ).
tcf(c_50536,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK9)))) = sK5(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_4619]) ).
tcf(c_50537,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK9)))) = sK5(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_4406]) ).
tcf(c_50538,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(sK5(sK1,relation_dom(sK9)),relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_12287]) ).
tcf(c_50560,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_9713,c_12789]) ).
tcf(c_50561,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_4763,c_12789]) ).
tcf(c_50565,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12789,c_87]) ).
tcf(c_50582,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50565,c_65,c_64]) ).
tcf(c_50605,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23369]) ).
tcf(c_50606,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23369]) ).
tcf(c_50607,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23369]) ).
tcf(c_50608,plain,
relation_inverse(relation_dom(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23369]) ).
tcf(c_50609,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23369]) ).
tcf(c_50610,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23369]) ).
tcf(c_50626,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23370]) ).
tcf(c_50627,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23370]) ).
tcf(c_50628,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23370]) ).
tcf(c_50629,plain,
relation_inverse(relation_dom(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23370]) ).
tcf(c_50630,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23370]) ).
tcf(c_50631,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23370]) ).
tcf(c_50711,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23371]) ).
tcf(c_50712,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23371]) ).
tcf(c_50713,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23371]) ).
tcf(c_50714,plain,
relation_inverse(relation_dom(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23371]) ).
tcf(c_50715,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23371]) ).
tcf(c_50716,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23371]) ).
tcf(c_50870,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23404]) ).
tcf(c_50871,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23404]) ).
tcf(c_50872,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23404]) ).
tcf(c_50873,plain,
relation_inverse(relation_dom(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23404]) ).
tcf(c_50874,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23404]) ).
tcf(c_50875,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23404]) ).
tcf(c_50895,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_50582]) ).
tcf(c_50896,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_50582]) ).
tcf(c_50897,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_50582,c_70]) ).
tcf(c_50898,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_50582,c_69]) ).
tcf(c_50900,plain,
( in(sK22(sK1,sK1),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_50582,c_106]) ).
tcf(c_50906,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_50900,c_4013]) ).
tcf(c_50932,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK2),sK6(sK1,relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_33533,c_70]) ).
tcf(c_50936,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_dom(sK9))) = apply(sK2,sK6(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_33533,c_42224]) ).
tcf(c_50937,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK9)))) = sK6(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_12701]) ).
tcf(c_50938,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_dom(sK9)))) = sK6(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_10144]) ).
tcf(c_50939,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK9))) = sK15(sK1,sK6(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_4468]) ).
tcf(c_50962,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK1),sK14(sK1,relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_33537,c_70]) ).
tcf(c_50966,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_dom(sK9))) = apply(sK1,sK14(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_12284]) ).
tcf(c_50967,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK9)))) = sK14(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_4619]) ).
tcf(c_50968,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK9)))) = sK14(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_4406]) ).
tcf(c_50987,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(relation_dom(sK2),sK13(sK1,relation_dom(sK9))) ),
inference(superposition,[status(thm)],[c_33539,c_70]) ).
tcf(c_50991,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_dom(sK9))) = apply(sK2,sK13(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_33539,c_42224]) ).
tcf(c_50992,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK9)))) = sK13(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_12701]) ).
tcf(c_50993,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_dom(sK9)))) = sK13(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_10144]) ).
tcf(c_50994,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK9))) = sK15(sK1,sK13(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_4468]) ).
tcf(c_50995,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ~ empty(relation_inverse(sK9))
| ~ in(sK13(sK1,relation_dom(sK9)),relation_dom(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_10148]) ).
tcf(c_51019,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_34013,c_79]) ).
tcf(c_51026,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_10510]) ).
tcf(c_51032,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_35530]) ).
tcf(c_51033,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34013,c_10207]) ).
tcf(c_51034,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_35870]) ).
tcf(c_51035,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_34013,c_10226]) ).
tcf(c_51036,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_36486]) ).
tcf(c_51037,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_34013,c_10228]) ).
tcf(c_51040,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_38367]) ).
tcf(c_51041,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_34013,c_10231]) ).
tcf(c_51059,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51019,c_4030]) ).
tcf(c_51060,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51059,c_3611]) ).
tcf(c_51120,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7060,c_12791]) ).
tcf(c_51121,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7472,c_12791]) ).
tcf(c_51125,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12791,c_87]) ).
tcf(c_51140,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51125,c_65,c_64]) ).
tcf(c_51163,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23405]) ).
tcf(c_51164,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23405]) ).
tcf(c_51165,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23405]) ).
tcf(c_51166,plain,
relation_inverse(relation_dom(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23405]) ).
tcf(c_51167,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23405]) ).
tcf(c_51168,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23405]) ).
tcf(c_51184,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23406]) ).
tcf(c_51185,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23406]) ).
tcf(c_51186,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23406]) ).
tcf(c_51187,plain,
relation_inverse(relation_dom(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23406]) ).
tcf(c_51188,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23406]) ).
tcf(c_51189,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23406]) ).
tcf(c_51205,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23518]) ).
tcf(c_51206,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23518]) ).
tcf(c_51207,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23518]) ).
tcf(c_51208,plain,
relation_inverse(relation_rng(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23518]) ).
tcf(c_51209,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23518]) ).
tcf(c_51210,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23518]) ).
tcf(c_51366,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23519]) ).
tcf(c_51367,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23519]) ).
tcf(c_51368,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23519]) ).
tcf(c_51369,plain,
relation_inverse(relation_rng(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23519]) ).
tcf(c_51370,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23519]) ).
tcf(c_51371,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23519]) ).
tcf(c_51393,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7241,c_51140]) ).
tcf(c_51394,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7060,c_51140]) ).
tcf(c_51395,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7472,c_51140]) ).
tcf(c_51396,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_51140,c_70]) ).
tcf(c_51397,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_51140,c_69]) ).
tcf(c_51399,plain,
( in(sK21(sK1,sK1),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_51140,c_106]) ).
tcf(c_51405,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51399,c_4013]) ).
tcf(c_51687,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23520]) ).
tcf(c_51688,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23520]) ).
tcf(c_51689,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23520]) ).
tcf(c_51690,plain,
relation_inverse(relation_rng(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23520]) ).
tcf(c_51691,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23520]) ).
tcf(c_51692,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23520]) ).
tcf(c_51732,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23555]) ).
tcf(c_51733,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23555]) ).
tcf(c_51734,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23555]) ).
tcf(c_51735,plain,
relation_inverse(relation_rng(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23555]) ).
tcf(c_51736,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23555]) ).
tcf(c_51737,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23555]) ).
tcf(c_51753,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23556]) ).
tcf(c_51754,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23556]) ).
tcf(c_51755,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23556]) ).
tcf(c_51756,plain,
relation_inverse(relation_rng(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23556]) ).
tcf(c_51757,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23556]) ).
tcf(c_51758,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23556]) ).
tcf(c_51774,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_23557]) ).
tcf(c_51775,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_23557]) ).
tcf(c_51776,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23557]) ).
tcf(c_51777,plain,
relation_inverse(relation_rng(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23557]) ).
tcf(c_51778,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_23557]) ).
tcf(c_51779,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_23557]) ).
tcf(c_52014,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_9987,c_12794]) ).
tcf(c_52015,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8130,c_12794]) ).
tcf(c_52019,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12794,c_87]) ).
tcf(c_52031,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52019,c_65,c_64]) ).
tcf(c_52051,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24297]) ).
tcf(c_52052,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24297]) ).
tcf(c_52053,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24297]) ).
tcf(c_52054,plain,
relation_inverse(relation_rng(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24297]) ).
tcf(c_52055,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24297]) ).
tcf(c_52056,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24297]) ).
tcf(c_52109,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24298]) ).
tcf(c_52110,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24298]) ).
tcf(c_52111,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24298]) ).
tcf(c_52112,plain,
relation_inverse(relation_rng(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24298]) ).
tcf(c_52113,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24298]) ).
tcf(c_52114,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24298]) ).
tcf(c_52130,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24299]) ).
tcf(c_52131,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24299]) ).
tcf(c_52132,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24299]) ).
tcf(c_52133,plain,
relation_inverse(relation_rng(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24299]) ).
tcf(c_52134,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24299]) ).
tcf(c_52135,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24299]) ).
tcf(c_52151,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24359]) ).
tcf(c_52152,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24359]) ).
tcf(c_52153,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24359]) ).
tcf(c_52154,plain,
relation_inverse(relation_inverse(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24359]) ).
tcf(c_52155,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24359]) ).
tcf(c_52156,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24359]) ).
tcf(c_52188,plain,
( in(ordered_pair(sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9987,c_52031]) ).
tcf(c_52189,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8130,c_52031]) ).
tcf(c_52190,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_52031,c_70]) ).
tcf(c_52191,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52031,c_69]) ).
tcf(c_52193,plain,
( in(sK13(sK1,empty_set),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52031,c_106]) ).
tcf(c_52196,plain,
( ( relation_dom(sK2) = empty_set )
| ( relation_rng(sK1) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,empty_set),empty_set)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52031,c_104]) ).
tcf(c_52200,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_52193,c_4013]) ).
tcf(c_52214,plain,
( ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,empty_set),empty_set)
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_52196,c_4013]) ).
tcf(c_52259,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = X0 )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_4044]) ).
tcf(c_52260,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK2,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)))) = ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_4044]) ).
tcf(c_52261,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(X0,sK7(relation_dom(sK2),X0)))) = ordered_pair(X0,sK7(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_4044]) ).
tcf(c_52262,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(X0,apply(relation_dom(sK2),X0)))) = 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_87,c_4044]) ).
tcf(c_52263,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK2,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)))) = ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_4044]) ).
tcf(c_52264,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK15(relation_dom(sK2),X0),X0))) = ordered_pair(sK15(relation_dom(sK2),X0),X0) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_4044]) ).
tcf(c_52265,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) = ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_4044]) ).
tcf(c_52266,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))))) = ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_4044]) ).
tcf(c_52267,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) = ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_4044]) ).
tcf(c_52268,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)))) = ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_4044]) ).
tcf(c_52270,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_38509,c_4044]) ).
tcf(c_52271,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_4546,c_4044]) ).
tcf(c_52272,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_4044]) ).
tcf(c_52273,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_4044]) ).
tcf(c_52275,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5275,c_4044]) ).
tcf(c_52276,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8548,c_4044]) ).
tcf(c_52277,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_6286,c_4044]) ).
tcf(c_52278,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8302,c_4044]) ).
tcf(c_52279,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5335,c_4044]) ).
tcf(c_52280,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK2,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_5141,c_4044]) ).
tcf(c_52281,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6280,c_4044]) ).
tcf(c_52282,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK6(sK1,X0))) = sK6(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_4044]) ).
tcf(c_52283,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5335,c_4044]) ).
tcf(c_52289,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_6330,c_4044]) ).
tcf(c_52290,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK13(sK1,X0))) = sK13(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_4044]) ).
tcf(c_52291,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5542,c_4044]) ).
tcf(c_52292,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_4044]) ).
tcf(c_52293,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_4044]) ).
tcf(c_52294,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_4044]) ).
tcf(c_52295,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_4044]) ).
tcf(c_52296,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_4044]) ).
tcf(c_52297,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_4044]) ).
tcf(c_52298,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_4044]) ).
tcf(c_52299,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_4044]) ).
tcf(c_52300,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_4044]) ).
tcf(c_52301,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_4044]) ).
tcf(c_52302,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_4044]) ).
tcf(c_52303,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_4044]) ).
tcf(c_52304,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_4044]) ).
tcf(c_52305,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_4044]) ).
tcf(c_52306,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_4044]) ).
tcf(c_52307,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_4044]) ).
tcf(c_52308,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8310,c_4044]) ).
tcf(c_52309,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_7149,c_4044]) ).
tcf(c_52310,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8306,c_4044]) ).
tcf(c_52311,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6706,c_4044]) ).
tcf(c_52312,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_6686,c_4044]) ).
tcf(c_52313,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8158,c_4044]) ).
tcf(c_52314,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8154,c_4044]) ).
tcf(c_52316,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8131,c_4044]) ).
tcf(c_52321,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_4044]) ).
tcf(c_52322,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_4044]) ).
tcf(c_52325,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4044]) ).
tcf(c_52326,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK2,relation_dom(sK2)))) = sK13(sK2,relation_dom(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4044]) ).
tcf(c_52327,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_4044]) ).
tcf(c_52328,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(sK1,apply(sK2,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_4044]) ).
tcf(c_52329,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_4044]) ).
tcf(c_52330,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_4044]) ).
tcf(c_52331,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_4044]) ).
tcf(c_52332,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = sK2 )
| ( apply(sK1,apply(sK2,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_4044]) ).
tcf(c_52333,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_4044]) ).
tcf(c_52334,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_4044]) ).
tcf(c_52335,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK22(sK2,sK1))) = sK22(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_4044]) ).
tcf(c_52336,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_4044]) ).
tcf(c_52337,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4044]) ).
tcf(c_52338,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4044]) ).
tcf(c_52339,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK15(sK2,X0))) = sK15(sK2,X0) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_4044]) ).
tcf(c_52340,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_4044]) ).
tcf(c_52341,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_4044]) ).
tcf(c_52342,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_4044]) ).
tcf(c_52343,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_4044]) ).
tcf(c_52344,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK2,sK2))) = sK21(sK2,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_4044]) ).
tcf(c_52345,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK14(sK2,empty_set))) = sK14(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_4044]) ).
tcf(c_52346,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(sK2,sK5(sK2,empty_set))) = sK5(sK2,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_4044]) ).
tcf(c_52347,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_dom(X0)))) = sK6(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_4044]) ).
tcf(c_52348,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_dom(X0)))) = sK13(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_4044]) ).
tcf(c_52349,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_rng(X0)))) = sK6(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_4044]) ).
tcf(c_52350,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_rng(X0)))) = sK13(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_4044]) ).
tcf(c_52351,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_rng(sK9)))) = sK6(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_4044]) ).
tcf(c_52352,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_rng(sK9)))) = sK13(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_4044]) ).
tcf(c_52353,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_4044]) ).
tcf(c_52354,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_4044]) ).
tcf(c_52355,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_4044]) ).
tcf(c_52356,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_4044]) ).
tcf(c_52358,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_dom(sK9)))) = sK6(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_4044]) ).
tcf(c_52359,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_dom(sK9)))) = sK13(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_4044]) ).
tcf(c_52360,plain,
( empty(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_36111,c_4044]) ).
tcf(c_52427,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52259,c_62,c_61]) ).
tcf(c_53280,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24360]) ).
tcf(c_53281,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24360]) ).
tcf(c_53282,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24360]) ).
tcf(c_53283,plain,
relation_inverse(relation_inverse(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24360]) ).
tcf(c_53284,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24360]) ).
tcf(c_53285,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24360]) ).
tcf(c_53301,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24361]) ).
tcf(c_53302,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24361]) ).
tcf(c_53303,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24361]) ).
tcf(c_53304,plain,
relation_inverse(relation_inverse(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24361]) ).
tcf(c_53305,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24361]) ).
tcf(c_53306,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24361]) ).
tcf(c_53396,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24396]) ).
tcf(c_53397,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24396]) ).
tcf(c_53398,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24396]) ).
tcf(c_53399,plain,
relation_inverse(relation_inverse(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24396]) ).
tcf(c_53400,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24396]) ).
tcf(c_53401,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24396]) ).
tcf(c_53417,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24397]) ).
tcf(c_53418,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24397]) ).
tcf(c_53419,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24397]) ).
tcf(c_53420,plain,
relation_inverse(relation_inverse(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24397]) ).
tcf(c_53421,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24397]) ).
tcf(c_53422,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24397]) ).
tcf(c_53444,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_87]) ).
tcf(c_53445,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,X0) = sK15(sK1,X0) )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,apply(sK2,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_52427,c_4863]) ).
tcf(c_53446,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(relation_dom(sK2),X0)
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_6246]) ).
tcf(c_53447,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_6247]) ).
tcf(c_53448,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_5332]) ).
tcf(c_53449,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ( apply(sK1,apply(sK2,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_52427,c_4791]) ).
tcf(c_53470,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53444,c_65,c_64]) ).
tcf(c_53557,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,X0),X0)) ),
inference(superposition,[status(thm)],[c_53470,c_70]) ).
tcf(c_53558,plain,
! [X0: $i] :
( element(ordered_pair(apply(sK2,X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_53470,c_69]) ).
tcf(c_53560,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_53470,c_106]) ).
tcf(c_53563,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(apply(sK2,sK13(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_53470,c_104]) ).
tcf(c_53566,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_53470,c_3784]) ).
tcf(c_53567,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_53560,c_4013]) ).
tcf(c_53581,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(apply(sK2,sK13(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_53563,c_4013]) ).
tcf(c_55392,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10244,c_13070]) ).
tcf(c_55428,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24398]) ).
tcf(c_55429,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24398]) ).
tcf(c_55430,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24398]) ).
tcf(c_55431,plain,
relation_inverse(relation_inverse(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24398]) ).
tcf(c_55432,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24398]) ).
tcf(c_55433,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24398]) ).
tcf(c_55592,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24510]) ).
tcf(c_55593,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24510]) ).
tcf(c_55594,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24510]) ).
tcf(c_55595,plain,
relation_inverse(relation_inverse(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24510]) ).
tcf(c_55596,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24510]) ).
tcf(c_55597,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24510]) ).
tcf(c_55613,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24511]) ).
tcf(c_55614,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24511]) ).
tcf(c_55615,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24511]) ).
tcf(c_55616,plain,
relation_inverse(relation_inverse(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24511]) ).
tcf(c_55617,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24511]) ).
tcf(c_55618,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24511]) ).
tcf(c_55634,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_24512]) ).
tcf(c_55635,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_24512]) ).
tcf(c_55636,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24512]) ).
tcf(c_55637,plain,
relation_inverse(relation_inverse(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24512]) ).
tcf(c_55638,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_24512]) ).
tcf(c_55639,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_24512]) ).
tcf(c_55723,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_5349]) ).
tcf(c_55724,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,apply(sK2,X0))) = sK15(sK1,sK7(sK1,apply(sK2,X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_5349]) ).
tcf(c_55725,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_5349]) ).
tcf(c_55726,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_5349]) ).
tcf(c_55727,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_5349]) ).
tcf(c_55728,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_5349]) ).
tcf(c_55729,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) = sK15(sK1,sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_5349]) ).
tcf(c_55730,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_5349]) ).
tcf(c_55731,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_5349]) ).
tcf(c_55732,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_5349]) ).
tcf(c_55733,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_5349]) ).
tcf(c_55734,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_3448,c_5349]) ).
tcf(c_55735,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0))) = sK15(sK1,sK7(sK1,apply(relation_inverse(sK1),X0))) ) ),
inference(superposition,[status(thm)],[c_34571,c_5349]) ).
tcf(c_55741,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8430,c_5349]) ).
tcf(c_55742,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_6336,c_5349]) ).
tcf(c_55743,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8298,c_5349]) ).
tcf(c_55744,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_5563,c_5349]) ).
tcf(c_55745,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_5542,c_5349]) ).
tcf(c_55746,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_5349]) ).
tcf(c_55747,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_5349]) ).
tcf(c_55748,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_5349]) ).
tcf(c_55749,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_5349]) ).
tcf(c_55750,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_5349]) ).
tcf(c_55751,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_5349]) ).
tcf(c_55752,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_5349]) ).
tcf(c_55753,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_5349]) ).
tcf(c_55754,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_5349]) ).
tcf(c_55755,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_5349]) ).
tcf(c_55756,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_5349]) ).
tcf(c_55757,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_5349]) ).
tcf(c_55758,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8318,c_5349]) ).
tcf(c_55759,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_9090,c_5349]) ).
tcf(c_55760,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8314,c_5349]) ).
tcf(c_55761,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8158,c_5349]) ).
tcf(c_55762,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8154,c_5349]) ).
tcf(c_55763,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK15(sK1,sK7(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8540,c_5349]) ).
tcf(c_55764,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK15(sK1,sK7(sK1,sK5(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_5349]) ).
tcf(c_55765,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK15(sK1,sK7(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8302,c_5349]) ).
tcf(c_55766,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK15(sK1,sK7(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8422,c_5349]) ).
tcf(c_55767,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK15(sK1,sK7(sK1,sK14(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_5349]) ).
tcf(c_55768,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK15(sK1,sK7(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8298,c_5349]) ).
tcf(c_55769,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,sK7(sK1,sK15(sK1,X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_5349]) ).
tcf(c_55770,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,X0))) = sK15(sK1,sK7(sK1,sK22(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_5349]) ).
tcf(c_55771,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1))) = sK15(sK1,sK7(sK1,sK21(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_5349]) ).
tcf(c_55772,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1))) = sK15(sK1,sK7(sK1,sK23(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_5349]) ).
tcf(c_55773,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0))) = sK15(sK1,sK7(sK1,sK23(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_5349]) ).
tcf(c_55774,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))) = sK15(sK1,sK7(sK1,sK14(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_8427,c_5349]) ).
tcf(c_55775,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_5349]) ).
tcf(c_55776,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_5349]) ).
tcf(c_55778,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_8873,c_5349]) ).
tcf(c_55779,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) ) ),
inference(superposition,[status(thm)],[c_8992,c_5349]) ).
tcf(c_55780,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) ) ),
inference(superposition,[status(thm)],[c_9083,c_5349]) ).
tcf(c_55782,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0))) = sK15(sK1,sK7(sK1,sK7(relation_inverse(sK1),X0))) ) ),
inference(superposition,[status(thm)],[c_34011,c_5349]) ).
tcf(c_55783,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK5(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_5349]) ).
tcf(c_55784,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK5(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_5349]) ).
tcf(c_55785,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_5349]) ).
tcf(c_55786,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1)))) = sK15(sK1,sK7(sK1,sK13(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_5349]) ).
tcf(c_55787,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_5349]) ).
tcf(c_55788,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = sK15(sK1,sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_5349]) ).
tcf(c_55789,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_5349]) ).
tcf(c_55790,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = sK15(sK1,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_5349]) ).
tcf(c_55791,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_5349]) ).
tcf(c_55792,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = sK15(sK1,sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_5349]) ).
tcf(c_55793,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(X0)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_5349]) ).
tcf(c_55794,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(X0)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_5349]) ).
tcf(c_55795,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(X0)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_5349]) ).
tcf(c_55796,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(X0)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_5349]) ).
tcf(c_55797,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK9)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_5349]) ).
tcf(c_55798,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK9)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_5349]) ).
tcf(c_55799,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_5349]) ).
tcf(c_55800,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_5349]) ).
tcf(c_55801,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_5349]) ).
tcf(c_55802,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_5349]) ).
tcf(c_55803,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK9)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_5349]) ).
tcf(c_55804,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK9)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_5349]) ).
tcf(c_55805,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1))))) = sK15(sK1,sK7(sK1,sK20(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_36111,c_5349]) ).
tcf(c_55855,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55723,c_65,c_64]) ).
tcf(c_56203,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK15(sK1,sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_55855,c_87]) ).
tcf(c_56204,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,sK7(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_55855,c_4726]) ).
tcf(c_56205,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_55855,c_34564]) ).
tcf(c_56206,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_55855,c_34565]) ).
tcf(c_56207,plain,
! [X0: $i] :
( in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_55855,c_34571]) ).
tcf(c_56208,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_55855,c_34529]) ).
tcf(c_56209,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_55855,c_12764]) ).
tcf(c_56210,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_55855,c_13488]) ).
tcf(c_56211,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_55855,c_12807]) ).
tcf(c_56212,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_55855,c_4623]) ).
tcf(c_56214,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_55855,c_6421]) ).
tcf(c_56215,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_55855,c_8771]) ).
tcf(c_56216,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_55855,c_8798]) ).
tcf(c_56217,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_55855,c_10033]) ).
tcf(c_56262,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK15(sK1,sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_56203,c_4030]) ).
tcf(c_56263,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK15(sK1,sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56262,c_987,c_3611]) ).
tcf(c_56443,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_56204,c_107]) ).
tcf(c_56448,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK1),X0)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56204,c_8391]) ).
tcf(c_56449,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56204,c_8392]) ).
tcf(c_56450,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56204,c_8294]) ).
tcf(c_56460,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_56443,c_4013]) ).
tcf(c_56470,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_56450]) ).
tcf(c_56474,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56470,c_62,c_61]) ).
tcf(c_56485,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0) ),
inference(superposition,[status(thm)],[c_56474,c_70]) ).
tcf(c_56486,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_69]) ).
tcf(c_56488,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1)) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK5(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_56474,c_76]) ).
tcf(c_56489,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56474,c_106]) ).
tcf(c_56490,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56474,c_78]) ).
tcf(c_56491,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK1),X0) = X1 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56474,c_197]) ).
tcf(c_56493,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0))) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK13(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_56474,c_104]) ).
tcf(c_56494,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0) ),
inference(superposition,[status(thm)],[c_56474,c_124]) ).
tcf(c_56495,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) = empty_set )
| ( apply(sK2,sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_56474,c_129]) ).
tcf(c_56496,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_56474,c_5349]) ).
tcf(c_56499,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_56474,c_4619]) ).
tcf(c_56500,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_56474,c_4406]) ).
tcf(c_56503,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_10578]) ).
tcf(c_56506,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK2,sK7(sK1,sK5(sK2,relation_dom(sK1)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_56474,c_43088]) ).
tcf(c_56594,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_6249]) ).
tcf(c_56595,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,apply(sK2,X0))) = sK15(sK1,apply(sK1,apply(sK2,X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_6249]) ).
tcf(c_56596,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_6249]) ).
tcf(c_56597,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_6249]) ).
tcf(c_56598,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_6249]) ).
tcf(c_56599,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_6249]) ).
tcf(c_56600,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) = sK15(sK1,apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_6249]) ).
tcf(c_56601,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_6249]) ).
tcf(c_56602,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_6249]) ).
tcf(c_56603,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_6249]) ).
tcf(c_56604,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_6249]) ).
tcf(c_56605,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_56474,c_6249]) ).
tcf(c_56606,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_3448,c_6249]) ).
tcf(c_56607,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))) = sK15(sK1,apply(sK1,apply(relation_inverse(sK1),X0))) ) ),
inference(superposition,[status(thm)],[c_34571,c_6249]) ).
tcf(c_56613,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8430,c_6249]) ).
tcf(c_56614,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_6336,c_6249]) ).
tcf(c_56615,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8298,c_6249]) ).
tcf(c_56616,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_5563,c_6249]) ).
tcf(c_56617,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_5542,c_6249]) ).
tcf(c_56618,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_6249]) ).
tcf(c_56619,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_6249]) ).
tcf(c_56620,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_6249]) ).
tcf(c_56621,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_6249]) ).
tcf(c_56622,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_6249]) ).
tcf(c_56623,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_6249]) ).
tcf(c_56624,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_6249]) ).
tcf(c_56625,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_6249]) ).
tcf(c_56626,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_6249]) ).
tcf(c_56627,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_6249]) ).
tcf(c_56628,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_6249]) ).
tcf(c_56629,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_6249]) ).
tcf(c_56630,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8318,c_6249]) ).
tcf(c_56631,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_9090,c_6249]) ).
tcf(c_56632,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8314,c_6249]) ).
tcf(c_56633,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK5(empty_set,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8158,c_6249]) ).
tcf(c_56634,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(empty_set,relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_8154,c_6249]) ).
tcf(c_56635,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK15(sK1,apply(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8540,c_6249]) ).
tcf(c_56636,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK15(sK1,apply(sK1,sK5(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_6249]) ).
tcf(c_56637,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK15(sK1,apply(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8302,c_6249]) ).
tcf(c_56638,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK15(sK1,apply(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8422,c_6249]) ).
tcf(c_56639,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK15(sK1,apply(sK1,sK14(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_6249]) ).
tcf(c_56640,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK15(sK1,apply(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_8298,c_6249]) ).
tcf(c_56641,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,apply(sK1,sK15(sK1,X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_6249]) ).
tcf(c_56642,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,X0))) = sK15(sK1,apply(sK1,sK22(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_6249]) ).
tcf(c_56643,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1))) = sK15(sK1,apply(sK1,sK21(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_6249]) ).
tcf(c_56644,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1))) = sK15(sK1,apply(sK1,sK23(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_6249]) ).
tcf(c_56645,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0))) = sK15(sK1,apply(sK1,sK23(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_6249]) ).
tcf(c_56646,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = sK15(sK1,apply(sK1,sK14(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_8427,c_6249]) ).
tcf(c_56647,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_6249]) ).
tcf(c_56648,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_6249]) ).
tcf(c_56650,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = sK15(sK1,apply(sK1,sK23(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_8873,c_6249]) ).
tcf(c_56651,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = sK15(sK1,apply(sK1,sK23(empty_set,sK1))) ) ),
inference(superposition,[status(thm)],[c_8992,c_6249]) ).
tcf(c_56652,plain,
( ( sK1 = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = sK15(sK1,apply(sK1,sK21(empty_set,sK1))) ) ),
inference(superposition,[status(thm)],[c_9083,c_6249]) ).
tcf(c_56654,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))) = sK15(sK1,apply(sK1,sK7(relation_inverse(sK1),X0))) ) ),
inference(superposition,[status(thm)],[c_34011,c_6249]) ).
tcf(c_56655,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK5(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_6249]) ).
tcf(c_56656,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK5(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_6249]) ).
tcf(c_56657,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_6249]) ).
tcf(c_56658,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK15(sK1,apply(sK1,sK13(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_6249]) ).
tcf(c_56659,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_6249]) ).
tcf(c_56660,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = sK15(sK1,apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_6249]) ).
tcf(c_56661,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_6249]) ).
tcf(c_56662,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = sK15(sK1,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_6249]) ).
tcf(c_56663,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_6249]) ).
tcf(c_56664,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = sK15(sK1,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_6249]) ).
tcf(c_56665,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(X0)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_6249]) ).
tcf(c_56666,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(X0)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_6249]) ).
tcf(c_56667,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(X0)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_6249]) ).
tcf(c_56668,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(X0)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_6249]) ).
tcf(c_56669,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK9)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_6249]) ).
tcf(c_56670,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK9)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_6249]) ).
tcf(c_56671,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_6249]) ).
tcf(c_56672,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_6249]) ).
tcf(c_56673,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_6249]) ).
tcf(c_56674,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_6249]) ).
tcf(c_56675,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK9)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_6249]) ).
tcf(c_56676,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK9)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_6249]) ).
tcf(c_56677,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK15(sK1,apply(sK1,sK20(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_36111,c_6249]) ).
tcf(c_56725,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56594,c_65,c_64]) ).
tcf(c_57158,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),empty_set) = sK15(sK1,empty_set) )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_56725]) ).
tcf(c_57184,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),sK15(sK1,apply(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_56725,c_87]) ).
tcf(c_57185,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_56725,c_34564]) ).
tcf(c_57186,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_56725,c_34565]) ).
tcf(c_57187,plain,
! [X0: $i] :
( in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_56725,c_34571]) ).
tcf(c_57188,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_56725,c_34529]) ).
tcf(c_57189,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56725,c_12764]) ).
tcf(c_57190,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56725,c_13488]) ).
tcf(c_57191,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56725,c_12807]) ).
tcf(c_57192,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56725,c_4623]) ).
tcf(c_57193,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK15(sK1,apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_56725,c_4791]) ).
tcf(c_57195,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_56725,c_6420]) ).
tcf(c_57196,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_56725,c_8770]) ).
tcf(c_57197,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(sK1,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_56725,c_8797]) ).
tcf(c_57198,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ( sK15(sK1,apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_56725,c_10032]) ).
tcf(c_57241,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),sK15(sK1,apply(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57184,c_4030]) ).
tcf(c_57242,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),sK15(sK1,apply(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57241,c_987,c_3611]) ).
tcf(c_57569,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25246]) ).
tcf(c_57570,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25246]) ).
tcf(c_57571,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25246]) ).
tcf(c_57572,plain,
sK20(powerset(relation_dom(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25246]) ).
tcf(c_57573,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25246]) ).
tcf(c_57574,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25246]) ).
tcf(c_57719,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25247]) ).
tcf(c_57720,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25247]) ).
tcf(c_57721,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25247]) ).
tcf(c_57722,plain,
sK20(powerset(relation_dom(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25247]) ).
tcf(c_57723,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25247]) ).
tcf(c_57724,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25247]) ).
tcf(c_57740,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25248]) ).
tcf(c_57741,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25248]) ).
tcf(c_57742,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25248]) ).
tcf(c_57743,plain,
sK20(powerset(relation_dom(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25248]) ).
tcf(c_57744,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25248]) ).
tcf(c_57745,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25248]) ).
tcf(c_57761,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25310]) ).
tcf(c_57762,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25310]) ).
tcf(c_57763,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25310]) ).
tcf(c_57764,plain,
sK20(powerset(relation_rng(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25310]) ).
tcf(c_57765,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25310]) ).
tcf(c_57766,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25310]) ).
tcf(c_57782,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,X0) = sK15(sK1,X0) )
| ( apply(sK1,apply(sK2,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_52427,c_57193]) ).
tcf(c_57785,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = sK15(sK1,empty_set) )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_57193]) ).
tcf(c_57786,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),X0) = sK15(sK1,X0) )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10201,c_57193]) ).
tcf(c_57789,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10207,c_57193]) ).
tcf(c_57790,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10226,c_57193]) ).
tcf(c_57791,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10228,c_57193]) ).
tcf(c_57793,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK13(sK1,empty_set)) = sK15(sK1,sK13(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10231,c_57193]) ).
tcf(c_57805,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_57193,c_107]) ).
tcf(c_57809,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK1),X0)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_57193,c_8391]) ).
tcf(c_57810,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_57193,c_8392]) ).
tcf(c_57811,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_57193,c_8294]) ).
tcf(c_57821,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57805,c_4013]) ).
tcf(c_57867,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_57811]) ).
tcf(c_57873,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52427,c_57811]) ).
tcf(c_57874,plain,
( in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8695,c_57811]) ).
tcf(c_57875,plain,
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12791,c_57811]) ).
tcf(c_57876,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13464,c_57811]) ).
tcf(c_57879,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10244,c_57811]) ).
tcf(c_57881,plain,
( in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10207,c_57811]) ).
tcf(c_57882,plain,
( in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10226,c_57811]) ).
tcf(c_57883,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10228,c_57811]) ).
tcf(c_57885,plain,
( in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10231,c_57811]) ).
tcf(c_57887,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12807,c_57811]) ).
tcf(c_57888,plain,
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12770,c_57811]) ).
tcf(c_57889,plain,
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12789,c_57811]) ).
tcf(c_57890,plain,
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12794,c_57811]) ).
tcf(c_57900,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57867,c_62,c_61]) ).
tcf(c_58008,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0) ),
inference(superposition,[status(thm)],[c_57900,c_70]) ).
tcf(c_58009,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_69]) ).
tcf(c_58011,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK5(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_57900,c_76]) ).
tcf(c_58012,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57900,c_106]) ).
tcf(c_58013,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57900,c_78]) ).
tcf(c_58014,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK1),X0) = X1 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57900,c_197]) ).
tcf(c_58016,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK13(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_57900,c_104]) ).
tcf(c_58017,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0) ),
inference(superposition,[status(thm)],[c_57900,c_124]) ).
tcf(c_58018,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_57900,c_129]) ).
tcf(c_58019,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_57900,c_6249]) ).
tcf(c_58020,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_57900,c_5349]) ).
tcf(c_58023,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_57900,c_4619]) ).
tcf(c_58024,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_57900,c_4406]) ).
tcf(c_58027,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_10578]) ).
tcf(c_58028,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK1,X0))) = empty_set )
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_57900,c_12287]) ).
tcf(c_58030,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK2,relation_dom(sK1)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_57900,c_43088]) ).
tcf(c_58131,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_8395]) ).
tcf(c_58132,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_8395]) ).
tcf(c_58133,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_8395]) ).
tcf(c_58134,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(X0,apply(relation_dom(sK2),X0))))) = sK15(sK1,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_87,c_8395]) ).
tcf(c_58135,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_8395]) ).
tcf(c_58136,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0)))) = sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_8395]) ).
tcf(c_58137,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8395]) ).
tcf(c_58138,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8395]) ).
tcf(c_58139,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8395]) ).
tcf(c_58140,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8395]) ).
tcf(c_58141,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_3448,c_8395]) ).
tcf(c_58142,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_38509,c_8395]) ).
tcf(c_58143,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_4546,c_8395]) ).
tcf(c_58144,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK7(sK1,X0)))) = sK15(sK1,sK7(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_8395]) ).
tcf(c_58145,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,apply(sK1,X0)))) = sK15(sK1,apply(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_8395]) ).
tcf(c_58147,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5275,c_8395]) ).
tcf(c_58148,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8548,c_8395]) ).
tcf(c_58149,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_6286,c_8395]) ).
tcf(c_58150,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8302,c_8395]) ).
tcf(c_58151,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5335,c_8395]) ).
tcf(c_58152,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5141,c_8395]) ).
tcf(c_58153,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6280,c_8395]) ).
tcf(c_58154,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_8395]) ).
tcf(c_58155,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5335,c_8395]) ).
tcf(c_58161,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6330,c_8395]) ).
tcf(c_58162,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_8395]) ).
tcf(c_58163,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5542,c_8395]) ).
tcf(c_58164,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_8395]) ).
tcf(c_58165,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_8395]) ).
tcf(c_58166,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_8395]) ).
tcf(c_58167,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(X0,sK1)))) = sK15(sK1,sK24(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_8395]) ).
tcf(c_58168,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_8395]) ).
tcf(c_58169,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_8395]) ).
tcf(c_58170,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_8395]) ).
tcf(c_58171,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,X0)))) = sK15(sK1,sK24(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_8395]) ).
tcf(c_58172,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_8395]) ).
tcf(c_58173,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_8395]) ).
tcf(c_58174,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_8395]) ).
tcf(c_58175,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(X0,sK1)))) = sK15(sK1,sK22(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_8395]) ).
tcf(c_58176,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_8395]) ).
tcf(c_58177,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_8395]) ).
tcf(c_58178,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_8395]) ).
tcf(c_58179,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_8395]) ).
tcf(c_58180,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8310,c_8395]) ).
tcf(c_58181,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7149,c_8395]) ).
tcf(c_58182,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8306,c_8395]) ).
tcf(c_58183,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_6706,c_8395]) ).
tcf(c_58184,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_6686,c_8395]) ).
tcf(c_58185,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2))))) = sK15(sK1,sK5(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8158,c_8395]) ).
tcf(c_58186,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2))))) = sK15(sK1,sK13(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8154,c_8395]) ).
tcf(c_58188,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,empty_set)))) = sK15(sK1,sK13(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8131,c_8395]) ).
tcf(c_58193,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_8395]) ).
tcf(c_58194,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_8395]) ).
tcf(c_58197,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2))))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8395]) ).
tcf(c_58198,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2))))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_8395]) ).
tcf(c_58199,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_8395]) ).
tcf(c_58200,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_8395]) ).
tcf(c_58201,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_8395]) ).
tcf(c_58202,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_8395]) ).
tcf(c_58203,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_8395]) ).
tcf(c_58204,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_8395]) ).
tcf(c_58205,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_8395]) ).
tcf(c_58206,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_8395]) ).
tcf(c_58207,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK2,sK1)))) = sK15(sK1,sK22(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_8395]) ).
tcf(c_58208,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK2)))) = sK15(sK1,sK21(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_8395]) ).
tcf(c_58209,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK2,X0)))) = sK15(sK1,sK5(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_8395]) ).
tcf(c_58210,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK14(sK2,X0)))) = sK15(sK1,sK14(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8395]) ).
tcf(c_58211,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK15(sK2,X0)))) = sK15(sK1,sK15(sK2,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_8395]) ).
tcf(c_58212,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_8395]) ).
tcf(c_58213,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_8395]) ).
tcf(c_58214,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_8395]) ).
tcf(c_58215,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_8395]) ).
tcf(c_58216,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK2,sK2)))) = sK15(sK1,sK21(sK2,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_8395]) ).
tcf(c_58217,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK14(sK2,empty_set)))) = sK15(sK1,sK14(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_8395]) ).
tcf(c_58218,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK2,empty_set)))) = sK15(sK1,sK5(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_8395]) ).
tcf(c_58219,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_dom(X0))))) = sK15(sK1,sK6(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_8395]) ).
tcf(c_58220,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_dom(X0))))) = sK15(sK1,sK13(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_8395]) ).
tcf(c_58221,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_rng(X0))))) = sK15(sK1,sK6(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_8395]) ).
tcf(c_58222,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_rng(X0))))) = sK15(sK1,sK13(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_8395]) ).
tcf(c_58223,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK9))))) = sK15(sK1,sK6(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_8395]) ).
tcf(c_58224,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK9))))) = sK15(sK1,sK13(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_8395]) ).
tcf(c_58225,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12))))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_8395]) ).
tcf(c_58226,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12))))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_8395]) ).
tcf(c_58227,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12))))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_8395]) ).
tcf(c_58228,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12))))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_8395]) ).
tcf(c_58230,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK9))))) = sK15(sK1,sK6(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_8395]) ).
tcf(c_58231,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK9))))) = sK15(sK1,sK13(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_8395]) ).
tcf(c_58232,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2)))))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_8395]) ).
tcf(c_58270,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58131,c_62,c_61]) ).
tcf(c_58843,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_58270,c_87]) ).
tcf(c_58844,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0)))) ),
inference(superposition,[status(thm)],[c_58270,c_34564]) ).
tcf(c_58845,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_58270,c_34565]) ).
tcf(c_58846,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_58270,c_34571]) ).
tcf(c_58847,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_58270,c_34529]) ).
tcf(c_58848,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(sK1,apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_58270,c_9713]) ).
tcf(c_58849,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_58270,c_13488]) ).
tcf(c_58850,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_58270,c_4623]) ).
tcf(c_58851,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(sK1,apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_58270,c_4763]) ).
tcf(c_58852,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( sK15(sK1,apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_58270,c_56725]) ).
tcf(c_58880,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_58843,c_4030]) ).
tcf(c_58881,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58880,c_987,c_3611]) ).
tcf(c_58980,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_8396]) ).
tcf(c_58981,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_8396]) ).
tcf(c_58982,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_8396]) ).
tcf(c_58983,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(X0,apply(relation_dom(sK2),X0))))) = sK15(sK1,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_87,c_8396]) ).
tcf(c_58984,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_8396]) ).
tcf(c_58985,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0)))) = sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0)) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_8396]) ).
tcf(c_58986,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8396]) ).
tcf(c_58987,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_8396]) ).
tcf(c_58988,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8396]) ).
tcf(c_58989,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_8396]) ).
tcf(c_58990,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_3448,c_8396]) ).
tcf(c_58991,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_38509,c_8396]) ).
tcf(c_58992,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_4546,c_8396]) ).
tcf(c_58993,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK7(sK1,X0)))) = sK15(sK1,sK7(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_8396]) ).
tcf(c_58994,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,apply(sK1,X0)))) = sK15(sK1,apply(sK1,X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_8396]) ).
tcf(c_58997,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8548,c_8396]) ).
tcf(c_58998,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_6286,c_8396]) ).
tcf(c_58999,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8302,c_8396]) ).
tcf(c_59000,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5335,c_8396]) ).
tcf(c_59001,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2))))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_5141,c_8396]) ).
tcf(c_59002,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6280,c_8396]) ).
tcf(c_59003,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_8396]) ).
tcf(c_59004,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5335,c_8396]) ).
tcf(c_59010,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_6330,c_8396]) ).
tcf(c_59011,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_8396]) ).
tcf(c_59012,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_5542,c_8396]) ).
tcf(c_59013,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_8396]) ).
tcf(c_59014,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_8396]) ).
tcf(c_59015,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_8396]) ).
tcf(c_59016,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(X0,sK1)))) = sK15(sK1,sK24(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_8396]) ).
tcf(c_59017,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_8396]) ).
tcf(c_59018,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_8396]) ).
tcf(c_59019,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_8396]) ).
tcf(c_59020,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,X0)))) = sK15(sK1,sK24(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_8396]) ).
tcf(c_59021,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_8396]) ).
tcf(c_59022,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_8396]) ).
tcf(c_59023,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_8396]) ).
tcf(c_59024,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(X0,sK1)))) = sK15(sK1,sK22(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_8396]) ).
tcf(c_59025,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_8396]) ).
tcf(c_59026,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_8396]) ).
tcf(c_59027,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_8396]) ).
tcf(c_59028,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_8396]) ).
tcf(c_59029,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8310,c_8396]) ).
tcf(c_59030,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_7149,c_8396]) ).
tcf(c_59031,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8306,c_8396]) ).
tcf(c_59032,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_6706,c_8396]) ).
tcf(c_59033,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_6686,c_8396]) ).
tcf(c_59034,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2))))) = sK15(sK1,sK5(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8158,c_8396]) ).
tcf(c_59035,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2))))) = sK15(sK1,sK13(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_8154,c_8396]) ).
tcf(c_59037,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,empty_set)))) = sK15(sK1,sK13(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8131,c_8396]) ).
tcf(c_59042,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_8396]) ).
tcf(c_59043,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_8396]) ).
tcf(c_59046,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2))))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8396]) ).
tcf(c_59047,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2))))) = sK15(sK1,sK13(sK2,relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_8396]) ).
tcf(c_59048,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_8396]) ).
tcf(c_59049,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))))) = sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_8396]) ).
tcf(c_59050,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_8396]) ).
tcf(c_59051,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_8396]) ).
tcf(c_59052,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_8396]) ).
tcf(c_59053,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))))) = sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_8396]) ).
tcf(c_59054,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_8396]) ).
tcf(c_59055,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_8396]) ).
tcf(c_59056,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK2,sK1)))) = sK15(sK1,sK22(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_8396]) ).
tcf(c_59057,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK2)))) = sK15(sK1,sK21(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_8396]) ).
tcf(c_59058,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK2,X0)))) = sK15(sK1,sK5(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_8396]) ).
tcf(c_59059,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK14(sK2,X0)))) = sK15(sK1,sK14(sK2,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_8396]) ).
tcf(c_59060,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK15(sK2,X0)))) = sK15(sK1,sK15(sK2,X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_8396]) ).
tcf(c_59061,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_8396]) ).
tcf(c_59062,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_8396]) ).
tcf(c_59063,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_8396]) ).
tcf(c_59064,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_8396]) ).
tcf(c_59065,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK2,sK2)))) = sK15(sK1,sK21(sK2,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_8396]) ).
tcf(c_59066,plain,
( ( relation_rng(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK14(sK2,empty_set)))) = sK15(sK1,sK14(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_8396]) ).
tcf(c_59067,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK2,empty_set)))) = sK15(sK1,sK5(sK2,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_8396]) ).
tcf(c_59068,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_dom(X0))))) = sK15(sK1,sK6(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_8396]) ).
tcf(c_59069,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_dom(X0))))) = sK15(sK1,sK13(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_8396]) ).
tcf(c_59070,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_rng(X0))))) = sK15(sK1,sK6(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_8396]) ).
tcf(c_59071,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_rng(X0))))) = sK15(sK1,sK13(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_8396]) ).
tcf(c_59072,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_rng(sK9))))) = sK15(sK1,sK6(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_8396]) ).
tcf(c_59073,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_rng(sK9))))) = sK15(sK1,sK13(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_8396]) ).
tcf(c_59074,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12))))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_8396]) ).
tcf(c_59075,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12))))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_8396]) ).
tcf(c_59076,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12))))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_8396]) ).
tcf(c_59077,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12))))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_8396]) ).
tcf(c_59079,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_dom(sK9))))) = sK15(sK1,sK6(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_8396]) ).
tcf(c_59080,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_dom(sK9))))) = sK15(sK1,sK13(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_8396]) ).
tcf(c_59081,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2)))))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_8396]) ).
tcf(c_59117,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58980,c_62,c_61]) ).
tcf(c_59703,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_59117,c_87]) ).
tcf(c_59704,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_59117,c_55855]) ).
tcf(c_59705,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0)))) ),
inference(superposition,[status(thm)],[c_59117,c_34564]) ).
tcf(c_59706,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_34565]) ).
tcf(c_59707,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_34571]) ).
tcf(c_59708,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_34529]) ).
tcf(c_59709,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = sK7(sK1,sK15(sK1,X0)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_12764]) ).
tcf(c_59710,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_9713]) ).
tcf(c_59711,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59117,c_13488]) ).
tcf(c_59712,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = sK7(sK1,sK15(sK1,X0)) )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_12807]) ).
tcf(c_59713,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_59117,c_4623]) ).
tcf(c_59714,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59117,c_4763]) ).
tcf(c_59748,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_59703,c_4030]) ).
tcf(c_59749,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_59748,c_987,c_3611]) ).
tcf(c_60035,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25311]) ).
tcf(c_60036,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25311]) ).
tcf(c_60037,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25311]) ).
tcf(c_60038,plain,
sK20(powerset(relation_rng(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25311]) ).
tcf(c_60039,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25311]) ).
tcf(c_60040,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25311]) ).
tcf(c_60056,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25312]) ).
tcf(c_60057,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25312]) ).
tcf(c_60058,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25312]) ).
tcf(c_60059,plain,
sK20(powerset(relation_rng(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25312]) ).
tcf(c_60060,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25312]) ).
tcf(c_60061,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25312]) ).
tcf(c_60077,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25345]) ).
tcf(c_60078,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25345]) ).
tcf(c_60079,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25345]) ).
tcf(c_60080,plain,
sK20(powerset(relation_inverse(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25345]) ).
tcf(c_60081,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25345]) ).
tcf(c_60082,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25345]) ).
tcf(c_60113,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25346]) ).
tcf(c_60114,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25346]) ).
tcf(c_60115,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25346]) ).
tcf(c_60116,plain,
sK20(powerset(relation_inverse(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25346]) ).
tcf(c_60117,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25346]) ).
tcf(c_60118,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25346]) ).
tcf(c_60152,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_10202]) ).
tcf(c_60153,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,apply(sK2,X0)))) = sK7(sK1,apply(sK2,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_10202]) ).
tcf(c_60154,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_10202]) ).
tcf(c_60155,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_10202]) ).
tcf(c_60156,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_10202]) ).
tcf(c_60157,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_10202]) ).
tcf(c_60158,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)))) = sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_10202]) ).
tcf(c_60159,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10202]) ).
tcf(c_60160,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10202]) ).
tcf(c_60161,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10202]) ).
tcf(c_60162,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10202]) ).
tcf(c_60163,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_57900,c_10202]) ).
tcf(c_60164,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56474,c_10202]) ).
tcf(c_60165,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1))))) = sK7(sK1,sK20(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_3448,c_10202]) ).
tcf(c_60166,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0)))) = sK7(sK1,apply(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34571,c_10202]) ).
tcf(c_60172,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8430,c_10202]) ).
tcf(c_60173,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_6336,c_10202]) ).
tcf(c_60174,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8298,c_10202]) ).
tcf(c_60175,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5563,c_10202]) ).
tcf(c_60176,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5542,c_10202]) ).
tcf(c_60177,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_10202]) ).
tcf(c_60178,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_10202]) ).
tcf(c_60179,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_10202]) ).
tcf(c_60180,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_10202]) ).
tcf(c_60181,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_10202]) ).
tcf(c_60182,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_10202]) ).
tcf(c_60183,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_10202]) ).
tcf(c_60184,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_10202]) ).
tcf(c_60185,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_10202]) ).
tcf(c_60186,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_10202]) ).
tcf(c_60187,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_10202]) ).
tcf(c_60188,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_10202]) ).
tcf(c_60189,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8318,c_10202]) ).
tcf(c_60190,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9090,c_10202]) ).
tcf(c_60191,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8314,c_10202]) ).
tcf(c_60192,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1))))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8158,c_10202]) ).
tcf(c_60193,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1))))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8154,c_10202]) ).
tcf(c_60194,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8540,c_10202]) ).
tcf(c_60195,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_10202]) ).
tcf(c_60196,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8302,c_10202]) ).
tcf(c_60197,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8422,c_10202]) ).
tcf(c_60198,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_10202]) ).
tcf(c_60199,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8298,c_10202]) ).
tcf(c_60200,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0)))) = sK7(sK1,sK15(sK1,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_10202]) ).
tcf(c_60201,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,X0)))) = sK7(sK1,sK22(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_10202]) ).
tcf(c_60202,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1)))) = sK7(sK1,sK21(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_10202]) ).
tcf(c_60203,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1)))) = sK7(sK1,sK23(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_10202]) ).
tcf(c_60204,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0)))) = sK7(sK1,sK23(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_10202]) ).
tcf(c_60205,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set)))) = sK7(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8427,c_10202]) ).
tcf(c_60206,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_10202]) ).
tcf(c_60207,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_10202]) ).
tcf(c_60209,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set)))) = sK7(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8873,c_10202]) ).
tcf(c_60210,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1)))) = sK7(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8992,c_10202]) ).
tcf(c_60211,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1)))) = sK7(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_9083,c_10202]) ).
tcf(c_60213,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0)))) = sK7(sK1,sK7(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34011,c_10202]) ).
tcf(c_60214,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1))))) = sK7(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_10202]) ).
tcf(c_60215,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1))))) = sK7(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_10202]) ).
tcf(c_60216,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1))))) = sK7(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10202]) ).
tcf(c_60217,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1))))) = sK7(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_10202]) ).
tcf(c_60218,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_10202]) ).
tcf(c_60219,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_10202]) ).
tcf(c_60220,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_10202]) ).
tcf(c_60221,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_10202]) ).
tcf(c_60222,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_10202]) ).
tcf(c_60223,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_10202]) ).
tcf(c_60224,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(X0))))) = sK7(sK1,sK5(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_10202]) ).
tcf(c_60225,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(X0))))) = sK7(sK1,sK14(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_10202]) ).
tcf(c_60226,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(X0))))) = sK7(sK1,sK5(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_10202]) ).
tcf(c_60227,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(X0))))) = sK7(sK1,sK14(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_10202]) ).
tcf(c_60228,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK9))))) = sK7(sK1,sK5(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_10202]) ).
tcf(c_60229,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK9))))) = sK7(sK1,sK14(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_10202]) ).
tcf(c_60230,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12))))) = sK7(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_10202]) ).
tcf(c_60231,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12))))) = sK7(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_10202]) ).
tcf(c_60232,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12))))) = sK7(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_10202]) ).
tcf(c_60233,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12))))) = sK7(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_10202]) ).
tcf(c_60234,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK9))))) = sK7(sK1,sK5(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_10202]) ).
tcf(c_60235,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK9))))) = sK7(sK1,sK14(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_10202]) ).
tcf(c_60236,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1)))))) = sK7(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_10202]) ).
tcf(c_60275,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60152,c_65,c_64]) ).
tcf(c_60732,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34013,c_60275]) ).
tcf(c_60736,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_87]) ).
tcf(c_60737,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_60275,c_57811]) ).
tcf(c_60738,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK7(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_60275,c_57193]) ).
tcf(c_60743,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK2),sK7(sK1,X0))
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_6246]) ).
tcf(c_60744,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_6247]) ).
tcf(c_60745,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_5332]) ).
tcf(c_60746,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK7(relation_inverse(sK1),sK7(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_60275,c_4791]) ).
tcf(c_60747,plain,
! [X0: $i] :
( ( sK7(sK1,X0) = empty_set )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK7(relation_inverse(sK1),sK7(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_60275,c_10494]) ).
tcf(c_60777,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60736,c_65,c_64]) ).
tcf(c_60848,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_60777]) ).
tcf(c_60849,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_60777,c_70]) ).
tcf(c_60850,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60777,c_69]) ).
tcf(c_60852,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60777,c_106]) ).
tcf(c_60857,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK7(relation_inverse(sK1),sK7(sK1,X0)) )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60777,c_3784]) ).
tcf(c_60858,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_60852,c_4013]) ).
tcf(c_61009,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_10203]) ).
tcf(c_61010,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,apply(sK2,X0)))) = apply(sK1,apply(sK2,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_10203]) ).
tcf(c_61011,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_10203]) ).
tcf(c_61012,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_10203]) ).
tcf(c_61013,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_10203]) ).
tcf(c_61014,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_10203]) ).
tcf(c_61015,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)))) = apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_10203]) ).
tcf(c_61016,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10203]) ).
tcf(c_61017,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_10203]) ).
tcf(c_61018,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10203]) ).
tcf(c_61019,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_10203]) ).
tcf(c_61020,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_57900,c_10203]) ).
tcf(c_61021,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56474,c_10203]) ).
tcf(c_61022,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1))))) = apply(sK1,sK20(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_3448,c_10203]) ).
tcf(c_61023,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0)))) = apply(sK1,apply(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34571,c_10203]) ).
tcf(c_61029,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8430,c_10203]) ).
tcf(c_61030,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_6336,c_10203]) ).
tcf(c_61031,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8298,c_10203]) ).
tcf(c_61032,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5563,c_10203]) ).
tcf(c_61033,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5542,c_10203]) ).
tcf(c_61034,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_10203]) ).
tcf(c_61035,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_10203]) ).
tcf(c_61036,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_10203]) ).
tcf(c_61037,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_10203]) ).
tcf(c_61038,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_10203]) ).
tcf(c_61039,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_10203]) ).
tcf(c_61040,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_10203]) ).
tcf(c_61041,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_10203]) ).
tcf(c_61042,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_10203]) ).
tcf(c_61043,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_10203]) ).
tcf(c_61044,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_10203]) ).
tcf(c_61045,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_10203]) ).
tcf(c_61046,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8318,c_10203]) ).
tcf(c_61047,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9090,c_10203]) ).
tcf(c_61048,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8314,c_10203]) ).
tcf(c_61049,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1))))) = apply(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8158,c_10203]) ).
tcf(c_61050,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1))))) = apply(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8154,c_10203]) ).
tcf(c_61051,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8540,c_10203]) ).
tcf(c_61052,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_10203]) ).
tcf(c_61053,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8302,c_10203]) ).
tcf(c_61054,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8422,c_10203]) ).
tcf(c_61055,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_10203]) ).
tcf(c_61056,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8298,c_10203]) ).
tcf(c_61057,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,X0)))) = apply(sK1,sK15(sK1,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_10203]) ).
tcf(c_61058,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,X0)))) = apply(sK1,sK22(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_10203]) ).
tcf(c_61059,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(X0,sK1)))) = apply(sK1,sK21(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_10203]) ).
tcf(c_61060,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(X0,sK1)))) = apply(sK1,sK23(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_10203]) ).
tcf(c_61061,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,X0)))) = apply(sK1,sK23(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_10203]) ).
tcf(c_61062,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set)))) = apply(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8427,c_10203]) ).
tcf(c_61063,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_10203]) ).
tcf(c_61064,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_10203]) ).
tcf(c_61066,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set)))) = apply(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8873,c_10203]) ).
tcf(c_61067,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1)))) = apply(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8992,c_10203]) ).
tcf(c_61068,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1)))) = apply(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_9083,c_10203]) ).
tcf(c_61070,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0)))) = apply(sK1,sK7(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34011,c_10203]) ).
tcf(c_61071,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1))))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_10203]) ).
tcf(c_61072,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1))))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_10203]) ).
tcf(c_61073,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1))))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_10203]) ).
tcf(c_61074,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1))))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_10203]) ).
tcf(c_61075,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_10203]) ).
tcf(c_61076,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_10203]) ).
tcf(c_61077,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_10203]) ).
tcf(c_61078,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_10203]) ).
tcf(c_61079,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_10203]) ).
tcf(c_61080,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_10203]) ).
tcf(c_61081,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(X0))))) = apply(sK1,sK5(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_10203]) ).
tcf(c_61082,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(X0))))) = apply(sK1,sK14(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_10203]) ).
tcf(c_61083,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(X0))))) = apply(sK1,sK5(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_10203]) ).
tcf(c_61084,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(X0))))) = apply(sK1,sK14(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_10203]) ).
tcf(c_61085,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK9))))) = apply(sK1,sK5(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_10203]) ).
tcf(c_61086,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK9))))) = apply(sK1,sK14(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_10203]) ).
tcf(c_61087,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12))))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_10203]) ).
tcf(c_61088,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12))))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_10203]) ).
tcf(c_61089,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12))))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_10203]) ).
tcf(c_61090,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12))))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_10203]) ).
tcf(c_61091,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK9))))) = apply(sK1,sK5(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_10203]) ).
tcf(c_61092,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK9))))) = apply(sK1,sK14(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_10203]) ).
tcf(c_61093,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1)))))) = apply(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_10203]) ).
tcf(c_61136,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_61009,c_65,c_64]) ).
tcf(c_61525,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34013,c_61136]) ).
tcf(c_61526,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_52427,c_61136]) ).
tcf(c_61530,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),empty_set)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_61136]) ).
tcf(c_61542,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_87]) ).
tcf(c_61543,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61136,c_57811]) ).
tcf(c_61544,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61136,c_57193]) ).
tcf(c_61549,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK2),apply(sK1,X0))
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_6246]) ).
tcf(c_61550,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_6247]) ).
tcf(c_61551,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_5332]) ).
tcf(c_61552,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK7(relation_inverse(sK1),apply(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61136,c_4791]) ).
tcf(c_61553,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK7(relation_inverse(sK1),apply(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_61136,c_10494]) ).
tcf(c_61586,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_61542,c_65,c_64]) ).
tcf(c_61786,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_25347]) ).
tcf(c_61787,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_25347]) ).
tcf(c_61788,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25347]) ).
tcf(c_61789,plain,
sK20(powerset(relation_inverse(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25347]) ).
tcf(c_61790,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_25347]) ).
tcf(c_61791,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_25347]) ).
tcf(c_61819,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_27399]) ).
tcf(c_61820,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_27399]) ).
tcf(c_61821,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_27399]) ).
tcf(c_61822,plain,
relation_inverse(sK20(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_27399]) ).
tcf(c_61823,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_27399]) ).
tcf(c_61824,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_27399]) ).
tcf(c_61994,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_27400]) ).
tcf(c_61995,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_27400]) ).
tcf(c_61996,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_27400]) ).
tcf(c_61997,plain,
relation_inverse(sK20(powerset(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_27400]) ).
tcf(c_61998,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_27400]) ).
tcf(c_61999,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_27400]) ).
tcf(c_62015,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_27401]) ).
tcf(c_62016,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_27401]) ).
tcf(c_62017,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_27401]) ).
tcf(c_62018,plain,
relation_inverse(sK20(powerset(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_27401]) ).
tcf(c_62019,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_27401]) ).
tcf(c_62020,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_27401]) ).
tcf(c_62038,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_61586]) ).
tcf(c_62068,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(sK2,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_61586]) ).
tcf(c_62069,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(sK2,sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_61586]) ).
tcf(c_62070,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12791,c_61586]) ).
tcf(c_62071,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_61586]) ).
tcf(c_62074,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_61586]) ).
tcf(c_62076,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_61586]) ).
tcf(c_62077,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_61586]) ).
tcf(c_62078,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_61586]) ).
tcf(c_62079,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10226,c_61586]) ).
tcf(c_62080,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10228,c_61586]) ).
tcf(c_62082,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10231,c_61586]) ).
tcf(c_62084,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_61586]) ).
tcf(c_62085,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_61586]) ).
tcf(c_62086,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12789,c_61586]) ).
tcf(c_62087,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12794,c_61586]) ).
tcf(c_62097,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_61586,c_70]) ).
tcf(c_62098,plain,
! [X0: $i] :
( element(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61586,c_69]) ).
tcf(c_62100,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61586,c_106]) ).
tcf(c_62105,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK7(relation_inverse(sK1),apply(sK1,X0)) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61586,c_3784]) ).
tcf(c_62106,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62100,c_4013]) ).
tcf(c_62239,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_10492]) ).
tcf(c_62242,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34011,c_10492]) ).
tcf(c_62247,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62239,c_65,c_64]) ).
tcf(c_62259,plain,
! [X0: $i] :
( empty(relation_dom(sK2))
| in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_62247,c_68]) ).
tcf(c_62274,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = empty_set ) ),
inference(superposition,[status(thm)],[c_34011,c_10493]) ).
tcf(c_62286,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK5(sK1,sK20(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_11849,c_70]) ).
tcf(c_62290,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,sK20(powerset(X0)))))) = apply(sK1,sK5(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_10203]) ).
tcf(c_62291,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,sK20(powerset(X0)))))) = sK7(sK1,sK5(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_10202]) ).
tcf(c_62292,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,sK20(powerset(X0))))) = sK15(sK1,apply(sK1,sK5(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_6249]) ).
tcf(c_62293,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,sK20(powerset(X0))))) = sK15(sK1,sK7(sK1,sK5(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_5349]) ).
tcf(c_62295,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,sK20(powerset(X0)))) = apply(sK1,sK5(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_12284]) ).
tcf(c_62296,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,sK20(powerset(X0))))) = sK5(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_4619]) ).
tcf(c_62297,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,sK20(powerset(X0))))) = sK5(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_4406]) ).
tcf(c_62298,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(sK5(sK1,sK20(powerset(X0))),sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_11849,c_12287]) ).
tcf(c_62337,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK6(sK1,sK20(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_11850,c_70]) ).
tcf(c_62341,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,sK20(powerset(X0)))))) = sK15(sK1,sK6(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_8396]) ).
tcf(c_62342,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,sK20(powerset(X0)))))) = sK15(sK1,sK6(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_8395]) ).
tcf(c_62343,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,sK20(powerset(X0))))) = sK6(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_4044]) ).
tcf(c_62344,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,sK20(powerset(X0)))) = apply(sK2,sK6(sK1,sK20(powerset(X0)))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_11850,c_42224]) ).
tcf(c_62345,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(X0))))) = sK6(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_12701]) ).
tcf(c_62346,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,sK20(powerset(X0))))) = sK6(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_10144]) ).
tcf(c_62347,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(X0)))) = sK15(sK1,sK6(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_4468]) ).
tcf(c_62392,plain,
( in(sK14(sK1,empty_set),relation_dom(sK1))
| ( sK20(powerset(empty_set)) = relation_dom(sK2) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14781,c_11852]) ).
tcf(c_62393,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK14(sK1,sK20(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_11852,c_70]) ).
tcf(c_62397,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,sK20(powerset(X0)))))) = apply(sK1,sK14(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_10203]) ).
tcf(c_62398,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,sK20(powerset(X0)))))) = sK7(sK1,sK14(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_10202]) ).
tcf(c_62399,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,sK20(powerset(X0))))) = sK15(sK1,apply(sK1,sK14(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_6249]) ).
tcf(c_62400,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,sK20(powerset(X0))))) = sK15(sK1,sK7(sK1,sK14(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_5349]) ).
tcf(c_62402,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,sK20(powerset(X0)))) = apply(sK1,sK14(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_12284]) ).
tcf(c_62403,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,sK20(powerset(X0))))) = sK14(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_4619]) ).
tcf(c_62404,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,sK20(powerset(X0))))) = sK14(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_4406]) ).
tcf(c_62462,plain,
( in(sK13(sK1,empty_set),relation_dom(sK2))
| ( sK20(powerset(empty_set)) = relation_dom(sK2) )
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_14781,c_11854]) ).
tcf(c_62463,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK13(sK1,sK20(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_11854,c_70]) ).
tcf(c_62467,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,sK20(powerset(X0)))))) = sK15(sK1,sK13(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_8396]) ).
tcf(c_62468,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,sK20(powerset(X0)))))) = sK15(sK1,sK13(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_8395]) ).
tcf(c_62469,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,sK20(powerset(X0))))) = sK13(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_4044]) ).
tcf(c_62470,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,sK20(powerset(X0)))) = apply(sK2,sK13(sK1,sK20(powerset(X0)))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_11854,c_42224]) ).
tcf(c_62471,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(X0))))) = sK13(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_12701]) ).
tcf(c_62472,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,sK20(powerset(X0))))) = sK13(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_10144]) ).
tcf(c_62473,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(X0)))) = sK15(sK1,sK13(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_4468]) ).
tcf(c_62474,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ~ empty(X0)
| ~ in(sK13(sK1,sK20(powerset(X0))),sK20(powerset(X0))) ),
inference(superposition,[status(thm)],[c_11854,c_10148]) ).
tcf(c_62553,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_9713,c_13383]) ).
tcf(c_62554,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_4763,c_13383]) ).
tcf(c_62558,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_87]) ).
tcf(c_62559,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_61586]) ).
tcf(c_62561,plain,
( in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13383,c_57811]) ).
tcf(c_62567,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK2),sK13(empty_set,relation_dom(sK2)))
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_6246]) ).
tcf(c_62568,plain,
( element(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_6247]) ).
tcf(c_62569,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_5332]) ).
tcf(c_62592,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62558,c_65,c_64]) ).
tcf(c_62665,plain,
( in(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_62592]) ).
tcf(c_62666,plain,
( in(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_62592]) ).
tcf(c_62667,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_62592,c_70]) ).
tcf(c_62668,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_62592,c_69]) ).
tcf(c_62670,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_62592,c_106]) ).
tcf(c_62676,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62670,c_4013]) ).
tcf(c_62717,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,X0)) = apply(sK1,sK15(sK1,X0)) )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_12335]) ).
tcf(c_62718,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK2),X0),X0)
| ( relation_dom(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,ordered_pair(sK5(relation_dom(sK2),X0),sK6(relation_dom(sK2),X0)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_77,c_12335]) ).
tcf(c_62719,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,ordered_pair(X0,sK7(relation_dom(sK2),X0)))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_dom(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_79,c_12335]) ).
tcf(c_62720,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(X0,apply(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,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_87,c_12335]) ).
tcf(c_62721,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK2),X0),X0)
| ( relation_rng(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,ordered_pair(sK14(relation_dom(sK2),X0),sK13(relation_dom(sK2),X0)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_105,c_12335]) ).
tcf(c_62722,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0))) = apply(sK1,sK15(sK1,ordered_pair(sK15(relation_dom(sK2),X0),X0))) )
| ~ relation(relation_dom(sK2))
| ~ in(X0,relation_rng(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_107,c_12335]) ).
tcf(c_62723,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK2),X0),sK22(relation_dom(sK2),X0)),X0)
| ( relation_inverse(relation_dom(sK2)) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),X0),sK21(relation_dom(sK2),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_12335]) ).
tcf(c_62724,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK2)),sK21(X0,relation_dom(sK2))),X0)
| ( relation_inverse(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(X0,relation_dom(sK2)),sK22(X0,relation_dom(sK2))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_125,c_12335]) ).
tcf(c_62725,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(X0,relation_dom(sK2)),sK24(X0,relation_dom(sK2))))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_12335]) ).
tcf(c_62726,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),X0),sK24(relation_dom(sK2),X0)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_130,c_12335]) ).
tcf(c_62727,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_3448,c_12335]) ).
tcf(c_62728,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,X0)) = apply(sK1,sK15(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_38509,c_12335]) ).
tcf(c_62729,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,X0)) = apply(sK1,sK15(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_4546,c_12335]) ).
tcf(c_62730,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,sK7(sK1,X0))) = apply(sK1,sK15(sK1,sK7(sK1,X0))) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_12335]) ).
tcf(c_62731,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,apply(sK1,X0))) = apply(sK1,sK15(sK1,apply(sK1,X0))) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_12335]) ).
tcf(c_62733,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_5275,c_12335]) ).
tcf(c_62734,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_8548,c_12335]) ).
tcf(c_62735,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_6286,c_12335]) ).
tcf(c_62736,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_8302,c_12335]) ).
tcf(c_62737,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_5335,c_12335]) ).
tcf(c_62738,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_5141,c_12335]) ).
tcf(c_62739,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,X0))) = apply(sK1,sK15(sK1,sK6(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_6280,c_12335]) ).
tcf(c_62740,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,X0))) = apply(sK1,sK15(sK1,sK6(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6281,c_12335]) ).
tcf(c_62741,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,X0))) = apply(sK1,sK15(sK1,sK6(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_5335,c_12335]) ).
tcf(c_62747,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,X0))) = apply(sK1,sK15(sK1,sK13(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_6330,c_12335]) ).
tcf(c_62748,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,X0))) = apply(sK1,sK15(sK1,sK13(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6331,c_12335]) ).
tcf(c_62749,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,X0))) = apply(sK1,sK15(sK1,sK13(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_5542,c_12335]) ).
tcf(c_62750,plain,
( in(sK23(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8327,c_12335]) ).
tcf(c_62751,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK2),sK1)) = sK23(relation_dom(sK2),sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5709,c_12335]) ).
tcf(c_62752,plain,
( in(sK24(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK1),sK24(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5669,c_12335]) ).
tcf(c_62753,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(X0,sK1))) = apply(sK1,sK15(sK1,sK24(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32648,c_12335]) ).
tcf(c_62754,plain,
( in(sK23(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8322,c_12335]) ).
tcf(c_62755,plain,
( ( relation_dom(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK2))) = sK23(sK1,relation_dom(sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5704,c_12335]) ).
tcf(c_62756,plain,
( in(sK24(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(sK1,relation_dom(sK2)),sK24(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5654,c_12335]) ).
tcf(c_62757,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,X0))) = apply(sK1,sK15(sK1,sK24(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_32618,c_12335]) ).
tcf(c_62758,plain,
( in(sK21(relation_dom(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8332,c_12335]) ).
tcf(c_62759,plain,
( ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK2),sK1)) = sK21(relation_dom(sK2),sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5969,c_12335]) ).
tcf(c_62760,plain,
( in(sK22(relation_dom(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK1),sK21(relation_dom(sK2),sK1)))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5929,c_12335]) ).
tcf(c_62761,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(X0,sK1))) = apply(sK1,sK15(sK1,sK22(X0,sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37875,c_12335]) ).
tcf(c_62762,plain,
( in(sK22(sK1,relation_dom(sK2)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8337,c_12335]) ).
tcf(c_62763,plain,
( ( relation_dom(sK2) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK2))) = sK22(sK1,relation_dom(sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5964,c_12335]) ).
tcf(c_62764,plain,
( in(sK21(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(sK1,relation_dom(sK2)),sK22(sK1,relation_dom(sK2))))) )
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_5914,c_12335]) ).
tcf(c_62765,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,X0))) = apply(sK1,sK15(sK1,sK21(sK1,X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36354,c_12335]) ).
tcf(c_62766,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8310,c_12335]) ).
tcf(c_62767,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_7149,c_12335]) ).
tcf(c_62768,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_8306,c_12335]) ).
tcf(c_62769,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_6706,c_12335]) ).
tcf(c_62770,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_6686,c_12335]) ).
tcf(c_62771,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(empty_set,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_8158,c_12335]) ).
tcf(c_62772,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(empty_set,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_8154,c_12335]) ).
tcf(c_62774,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,empty_set))) = apply(sK1,sK15(sK1,sK13(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_8131,c_12335]) ).
tcf(c_62779,plain,
( in(sK23(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_12335]) ).
tcf(c_62780,plain,
( in(sK24(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK23(sK2,relation_dom(sK2)),sK24(sK2,relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_12335]) ).
tcf(c_62781,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,sK20(powerset(X0))))) = apply(sK1,sK15(sK1,sK6(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11850,c_12335]) ).
tcf(c_62782,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,sK20(powerset(X0))))) = apply(sK1,sK15(sK1,sK13(sK1,sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11854,c_12335]) ).
tcf(c_62785,plain,
( in(sK14(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK2,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12335]) ).
tcf(c_62786,plain,
( in(sK13(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK2,relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_12335]) ).
tcf(c_62787,plain,
( in(sK22(sK2,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_12335]) ).
tcf(c_62788,plain,
( in(sK21(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_inverse(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) = apply(sK1,sK15(sK1,ordered_pair(sK21(sK2,relation_dom(sK2)),sK22(sK2,relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_12335]) ).
tcf(c_62789,plain,
( in(sK21(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_12335]) ).
tcf(c_62790,plain,
( in(sK22(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK2)) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) = apply(sK1,sK15(sK1,ordered_pair(sK22(relation_dom(sK2),sK2),sK21(relation_dom(sK2),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_12335]) ).
tcf(c_62791,plain,
( in(sK23(relation_dom(sK2),sK2),relation_dom(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_12335]) ).
tcf(c_62792,plain,
( in(sK24(relation_dom(sK2),sK2),relation_rng(sK2))
| ( relation_dom(sK2) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) = apply(sK1,sK15(sK1,ordered_pair(sK23(relation_dom(sK2),sK2),sK24(relation_dom(sK2),sK2)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_12335]) ).
tcf(c_62793,plain,
( in(sK23(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23699,c_12335]) ).
tcf(c_62794,plain,
( in(sK23(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23689,c_12335]) ).
tcf(c_62795,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1))) = apply(sK1,sK15(sK1,sK22(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23677,c_12335]) ).
tcf(c_62796,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2))) = apply(sK1,sK15(sK1,sK21(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23673,c_12335]) ).
tcf(c_62797,plain,
! [X0: $i] :
( in(sK5(sK2,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK2,X0))) = apply(sK1,sK15(sK1,sK5(sK2,X0))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_12335]) ).
tcf(c_62798,plain,
! [X0: $i] :
( in(sK13(sK2,X0),X0)
| ( relation_rng(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK14(sK2,X0))) = apply(sK1,sK15(sK1,sK14(sK2,X0))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12335]) ).
tcf(c_62799,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,sK15(sK2,X0))) = apply(sK1,sK15(sK1,sK15(sK2,X0))) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_23681,c_12335]) ).
tcf(c_62800,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK23(sK2,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23740,c_12335]) ).
tcf(c_62801,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23704,c_12335]) ).
tcf(c_62802,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK23(sK1,sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23735,c_12335]) ).
tcf(c_62803,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23694,c_12335]) ).
tcf(c_62804,plain,
( in(sK22(sK2,sK2),relation_dom(sK2))
| ( relation_inverse(sK2) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK2,sK2))) = apply(sK1,sK15(sK1,sK21(sK2,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_26063,c_12335]) ).
tcf(c_62805,plain,
( ( relation_rng(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK14(sK2,empty_set))) = apply(sK1,sK15(sK1,sK14(sK2,empty_set))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24577,c_12335]) ).
tcf(c_62806,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK2,empty_set))) = apply(sK1,sK15(sK1,sK5(sK2,empty_set))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24805,c_12335]) ).
tcf(c_62807,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_dom(X0)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29857,c_12335]) ).
tcf(c_62808,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_dom(X0)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29868,c_12335]) ).
tcf(c_62809,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_rng(X0)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30437,c_12335]) ).
tcf(c_62810,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_rng(X0)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30446,c_12335]) ).
tcf(c_62811,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_rng(sK9)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32145,c_12335]) ).
tcf(c_62812,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_rng(sK9)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32149,c_12335]) ).
tcf(c_62813,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_rng(sK12)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32764,c_12335]) ).
tcf(c_62814,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_rng(sK12)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32770,c_12335]) ).
tcf(c_62815,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_dom(sK12)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32994,c_12335]) ).
tcf(c_62816,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_dom(sK12)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32999,c_12335]) ).
tcf(c_62818,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_dom(sK9)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33533,c_12335]) ).
tcf(c_62819,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_dom(sK9)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33539,c_12335]) ).
tcf(c_62820,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(sK19(relation_dom(sK2))))) = apply(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_36111,c_12335]) ).
tcf(c_62859,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,X0)) = apply(sK1,sK15(sK1,X0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62717,c_62,c_61]) ).
tcf(c_63418,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK15(sK1,X0),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_62859,c_107]) ).
tcf(c_63419,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_62859,c_4472]) ).
tcf(c_63423,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_63418,c_3821]) ).
tcf(c_63424,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,sK15(sK1,X0)),sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63423,c_3611]) ).
tcf(c_63436,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_12599]) ).
tcf(c_63437,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_12599]) ).
tcf(c_63438,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12791,c_12599]) ).
tcf(c_63439,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_12599]) ).
tcf(c_63442,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_12599]) ).
tcf(c_63444,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_12599]) ).
tcf(c_63445,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_12599]) ).
tcf(c_63446,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_12599]) ).
tcf(c_63447,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10226,c_12599]) ).
tcf(c_63448,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10228,c_12599]) ).
tcf(c_63450,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10231,c_12599]) ).
tcf(c_63452,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_12599]) ).
tcf(c_63453,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_12599]) ).
tcf(c_63454,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12789,c_12599]) ).
tcf(c_63455,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12794,c_12599]) ).
tcf(c_63456,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_12599]) ).
tcf(c_63466,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1))
| ~ in(sK1,ordered_pair(X0,apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_12599,c_70]) ).
tcf(c_63467,plain,
! [X0: $i] :
( element(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12599,c_69]) ).
tcf(c_63469,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12599,c_76]) ).
tcf(c_63470,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12599,c_106]) ).
tcf(c_63474,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12599,c_4237]) ).
tcf(c_63485,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_63470,c_4013]) ).
tcf(c_63645,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2))
| ~ in(sK1,ordered_pair(sK15(sK1,X0),X0)) ),
inference(superposition,[status(thm)],[c_12678,c_70]) ).
tcf(c_63646,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12678,c_69]) ).
tcf(c_63648,plain,
! [X0: $i] :
( in(X0,relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12678,c_106]) ).
tcf(c_63649,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12678,c_78]) ).
tcf(c_63651,plain,
! [X0: $i] :
( ( relation_rng(sK1) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12678,c_104]) ).
tcf(c_63652,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12678,c_4259]) ).
tcf(c_63666,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK13(sK1,X0),X0)
| ~ in(sK13(sK1,X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_63651,c_4013]) ).
tcf(c_63673,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_12765]) ).
tcf(c_63674,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,apply(sK2,X0)))) = sK7(sK1,apply(sK2,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_12765]) ).
tcf(c_63675,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_12765]) ).
tcf(c_63676,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_12765]) ).
tcf(c_63677,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_12765]) ).
tcf(c_63678,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_12765]) ).
tcf(c_63679,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)))) = sK7(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_12765]) ).
tcf(c_63680,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12765]) ).
tcf(c_63681,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12765]) ).
tcf(c_63682,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12765]) ).
tcf(c_63683,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12765]) ).
tcf(c_63684,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_57900,c_12765]) ).
tcf(c_63685,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56474,c_12765]) ).
tcf(c_63686,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1))))) = sK7(sK1,sK20(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_3448,c_12765]) ).
tcf(c_63687,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0)))) = sK7(sK1,apply(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34571,c_12765]) ).
tcf(c_63693,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8430,c_12765]) ).
tcf(c_63694,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_6336,c_12765]) ).
tcf(c_63695,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8298,c_12765]) ).
tcf(c_63696,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5563,c_12765]) ).
tcf(c_63697,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5542,c_12765]) ).
tcf(c_63698,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_12765]) ).
tcf(c_63699,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_12765]) ).
tcf(c_63700,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_12765]) ).
tcf(c_63701,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_12765]) ).
tcf(c_63702,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_12765]) ).
tcf(c_63703,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_12765]) ).
tcf(c_63704,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_12765]) ).
tcf(c_63705,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_12765]) ).
tcf(c_63706,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_12765]) ).
tcf(c_63707,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_12765]) ).
tcf(c_63708,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_12765]) ).
tcf(c_63709,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_12765]) ).
tcf(c_63710,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8318,c_12765]) ).
tcf(c_63711,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9090,c_12765]) ).
tcf(c_63712,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8314,c_12765]) ).
tcf(c_63713,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1))))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8158,c_12765]) ).
tcf(c_63714,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1))))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8154,c_12765]) ).
tcf(c_63715,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8540,c_12765]) ).
tcf(c_63716,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_12765]) ).
tcf(c_63717,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8302,c_12765]) ).
tcf(c_63718,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8422,c_12765]) ).
tcf(c_63719,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_12765]) ).
tcf(c_63720,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8298,c_12765]) ).
tcf(c_63721,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0)))) = sK7(sK1,sK15(sK1,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_12765]) ).
tcf(c_63722,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,X0)))) = sK7(sK1,sK22(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_12765]) ).
tcf(c_63723,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1)))) = sK7(sK1,sK21(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_12765]) ).
tcf(c_63724,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1)))) = sK7(sK1,sK23(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_12765]) ).
tcf(c_63725,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0)))) = sK7(sK1,sK23(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_12765]) ).
tcf(c_63726,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set)))) = sK7(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8427,c_12765]) ).
tcf(c_63727,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_12765]) ).
tcf(c_63728,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_12765]) ).
tcf(c_63730,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set)))) = sK7(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8873,c_12765]) ).
tcf(c_63731,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1)))) = sK7(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8992,c_12765]) ).
tcf(c_63732,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1)))) = sK7(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_9083,c_12765]) ).
tcf(c_63734,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0)))) = sK7(sK1,sK7(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34011,c_12765]) ).
tcf(c_63735,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,sK20(powerset(X0)))))) = sK7(sK1,sK5(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_12765]) ).
tcf(c_63736,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,sK20(powerset(X0)))))) = sK7(sK1,sK14(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_12765]) ).
tcf(c_63737,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1))))) = sK7(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_12765]) ).
tcf(c_63738,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1))))) = sK7(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_12765]) ).
tcf(c_63739,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1))))) = sK7(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12765]) ).
tcf(c_63740,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK13(sK2,relation_dom(sK1))))) = sK7(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_12765]) ).
tcf(c_63741,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_12765]) ).
tcf(c_63742,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = sK7(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_12765]) ).
tcf(c_63743,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_12765]) ).
tcf(c_63744,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_12765]) ).
tcf(c_63745,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_12765]) ).
tcf(c_63746,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = sK7(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_12765]) ).
tcf(c_63747,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(X0))))) = sK7(sK1,sK5(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_12765]) ).
tcf(c_63748,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(X0))))) = sK7(sK1,sK14(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_12765]) ).
tcf(c_63749,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(X0))))) = sK7(sK1,sK5(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_12765]) ).
tcf(c_63750,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(X0))))) = sK7(sK1,sK14(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_12765]) ).
tcf(c_63751,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK9))))) = sK7(sK1,sK5(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_12765]) ).
tcf(c_63752,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK9))))) = sK7(sK1,sK14(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_12765]) ).
tcf(c_63753,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12))))) = sK7(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_12765]) ).
tcf(c_63754,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12))))) = sK7(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_12765]) ).
tcf(c_63755,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12))))) = sK7(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_12765]) ).
tcf(c_63756,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12))))) = sK7(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_12765]) ).
tcf(c_63757,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK9))))) = sK7(sK1,sK5(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_12765]) ).
tcf(c_63758,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK9))))) = sK7(sK1,sK14(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_12765]) ).
tcf(c_63759,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1)))))) = sK7(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_12765]) ).
tcf(c_63810,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_63673,c_65,c_64]) ).
tcf(c_64168,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_55855,c_63810]) ).
tcf(c_64169,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_4726,c_63810]) ).
tcf(c_64172,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_6421,c_63810]) ).
tcf(c_64173,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = sK7(sK1,sK15(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_59117,c_63810]) ).
tcf(c_64174,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8771,c_63810]) ).
tcf(c_64175,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8798,c_63810]) ).
tcf(c_64176,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = sK7(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_10033,c_63810]) ).
tcf(c_64184,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_87]) ).
tcf(c_64185,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_12599]) ).
tcf(c_64186,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_61586]) ).
tcf(c_64188,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_63810,c_57811]) ).
tcf(c_64194,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK2),sK7(sK1,X0))
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_6246]) ).
tcf(c_64195,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_6247]) ).
tcf(c_64196,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_5332]) ).
tcf(c_64231,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_64184,c_65,c_64]) ).
tcf(c_64507,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_55855,c_64231]) ).
tcf(c_64508,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4726,c_64231]) ).
tcf(c_64511,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6421,c_64231]) ).
tcf(c_64512,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),sK7(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59117,c_64231]) ).
tcf(c_64513,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8771,c_64231]) ).
tcf(c_64514,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8798,c_64231]) ).
tcf(c_64515,plain,
( in(ordered_pair(sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10033,c_64231]) ).
tcf(c_64520,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_64231,c_70]) ).
tcf(c_64521,plain,
! [X0: $i] :
( element(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64231,c_69]) ).
tcf(c_64523,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64231,c_106]) ).
tcf(c_64532,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64523,c_4013]) ).
tcf(c_64592,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34013,c_13385]) ).
tcf(c_64596,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_87]) ).
tcf(c_64597,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_12599]) ).
tcf(c_64598,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_61586]) ).
tcf(c_64599,plain,
( in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13385,c_57811]) ).
tcf(c_64600,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = sK15(sK1,sK13(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13385,c_57193]) ).
tcf(c_64605,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK2),sK13(empty_set,relation_dom(sK2)))
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_6246]) ).
tcf(c_64606,plain,
( element(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_6247]) ).
tcf(c_64607,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_5332]) ).
tcf(c_64608,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13385,c_4791]) ).
tcf(c_64609,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK13(empty_set,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_13385,c_10494]) ).
tcf(c_64635,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_64596,c_65,c_64]) ).
tcf(c_64686,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34255]) ).
tcf(c_64687,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34255]) ).
tcf(c_64688,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34255]) ).
tcf(c_64689,plain,
relation_rng(sK20(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34255]) ).
tcf(c_64690,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34255]) ).
tcf(c_64691,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34255]) ).
tcf(c_64730,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34256]) ).
tcf(c_64731,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34256]) ).
tcf(c_64732,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34256]) ).
tcf(c_64733,plain,
relation_rng(sK20(powerset(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34256]) ).
tcf(c_64734,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34256]) ).
tcf(c_64735,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34256]) ).
tcf(c_64751,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34257]) ).
tcf(c_64752,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34257]) ).
tcf(c_64753,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34257]) ).
tcf(c_64754,plain,
relation_rng(sK20(powerset(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34257]) ).
tcf(c_64755,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34257]) ).
tcf(c_64756,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34257]) ).
tcf(c_64889,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_64635]) ).
tcf(c_64890,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_64635,c_70]) ).
tcf(c_64891,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64635,c_69]) ).
tcf(c_64893,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64635,c_106]) ).
tcf(c_64898,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64635,c_3784]) ).
tcf(c_64899,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64893,c_4013]) ).
tcf(c_64918,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64169,c_79]) ).
tcf(c_64919,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64169,c_64231]) ).
tcf(c_64920,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_64169,c_63810]) ).
tcf(c_64921,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64169,c_60777]) ).
tcf(c_64926,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64169,c_10690]) ).
tcf(c_64928,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64169,c_5347]) ).
tcf(c_64931,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_64169,c_6421]) ).
tcf(c_64933,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_64169,c_8771]) ).
tcf(c_64934,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_64169,c_8798]) ).
tcf(c_64935,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_64169,c_10033]) ).
tcf(c_64981,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,apply(sK2,X0)))) = apply(sK1,apply(sK2,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_12766]) ).
tcf(c_64982,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_12766]) ).
tcf(c_64983,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_12766]) ).
tcf(c_64984,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0))) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_12766]) ).
tcf(c_64985,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_12766]) ).
tcf(c_64986,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)))) = apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_12766]) ).
tcf(c_64987,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12766]) ).
tcf(c_64988,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_12766]) ).
tcf(c_64989,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12766]) ).
tcf(c_64990,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_12766]) ).
tcf(c_64991,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_57900,c_12766]) ).
tcf(c_64992,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_56474,c_12766]) ).
tcf(c_64993,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1))))) = apply(sK1,sK20(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_3448,c_12766]) ).
tcf(c_64994,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0)))) = apply(sK1,apply(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34571,c_12766]) ).
tcf(c_65000,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8430,c_12766]) ).
tcf(c_65001,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_6336,c_12766]) ).
tcf(c_65002,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8298,c_12766]) ).
tcf(c_65003,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5563,c_12766]) ).
tcf(c_65004,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_5542,c_12766]) ).
tcf(c_65005,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_12766]) ).
tcf(c_65006,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_12766]) ).
tcf(c_65007,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_12766]) ).
tcf(c_65008,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_12766]) ).
tcf(c_65009,plain,
( ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_12766]) ).
tcf(c_65010,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_12766]) ).
tcf(c_65011,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_12766]) ).
tcf(c_65012,plain,
( ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_12766]) ).
tcf(c_65013,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_12766]) ).
tcf(c_65014,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_12766]) ).
tcf(c_65015,plain,
( ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_12766]) ).
tcf(c_65016,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1)))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_12766]) ).
tcf(c_65017,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8318,c_12766]) ).
tcf(c_65018,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_9090,c_12766]) ).
tcf(c_65019,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_8314,c_12766]) ).
tcf(c_65020,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1))))) = apply(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8158,c_12766]) ).
tcf(c_65021,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1))))) = apply(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_8154,c_12766]) ).
tcf(c_65022,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8540,c_12766]) ).
tcf(c_65023,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_12766]) ).
tcf(c_65024,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8302,c_12766]) ).
tcf(c_65025,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8422,c_12766]) ).
tcf(c_65026,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_12766]) ).
tcf(c_65027,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_8298,c_12766]) ).
tcf(c_65028,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0)))) = apply(sK1,sK15(sK1,X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_12766]) ).
tcf(c_65029,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,X0)))) = apply(sK1,sK22(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_12766]) ).
tcf(c_65030,plain,
! [X0: $i] :
( ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1)))) = apply(sK1,sK21(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_12766]) ).
tcf(c_65031,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1)))) = apply(sK1,sK23(X0,sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_12766]) ).
tcf(c_65032,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0)))) = apply(sK1,sK23(sK1,X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_12766]) ).
tcf(c_65033,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set)))) = apply(sK1,sK14(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8427,c_12766]) ).
tcf(c_65034,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_12766]) ).
tcf(c_65035,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_12766]) ).
tcf(c_65037,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set)))) = apply(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_8873,c_12766]) ).
tcf(c_65038,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1)))) = apply(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_8992,c_12766]) ).
tcf(c_65039,plain,
( ( sK1 = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1)))) = apply(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_9083,c_12766]) ).
tcf(c_65041,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0)))) = apply(sK1,sK7(relation_inverse(sK1),X0)) ) ),
inference(superposition,[status(thm)],[c_34011,c_12766]) ).
tcf(c_65042,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,sK20(powerset(X0)))))) = apply(sK1,sK5(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_12766]) ).
tcf(c_65043,plain,
! [X0: $i] :
( ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,sK20(powerset(X0)))))) = apply(sK1,sK14(sK1,sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_12766]) ).
tcf(c_65044,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1))))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_12766]) ).
tcf(c_65045,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1))))) = apply(sK1,sK5(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_12766]) ).
tcf(c_65046,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1))))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_12766]) ).
tcf(c_65047,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK13(sK2,relation_dom(sK1))))) = apply(sK1,sK13(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_12766]) ).
tcf(c_65048,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_12766]) ).
tcf(c_65049,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))))) = apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1)))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_12766]) ).
tcf(c_65050,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_12766]) ).
tcf(c_65051,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_12766]) ).
tcf(c_65052,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_12766]) ).
tcf(c_65053,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_dom(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))))) = apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_12766]) ).
tcf(c_65054,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(X0))))) = apply(sK1,sK5(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_12766]) ).
tcf(c_65055,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(X0))))) = apply(sK1,sK14(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_12766]) ).
tcf(c_65056,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(X0))))) = apply(sK1,sK5(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_12766]) ).
tcf(c_65057,plain,
! [X0: $i] :
( ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(X0))))) = apply(sK1,sK14(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_12766]) ).
tcf(c_65058,plain,
( ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK9))))) = apply(sK1,sK5(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_12766]) ).
tcf(c_65059,plain,
( ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK9))))) = apply(sK1,sK14(sK1,relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_12766]) ).
tcf(c_65060,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12))))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_12766]) ).
tcf(c_65061,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12))))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_12766]) ).
tcf(c_65062,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12))))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_12766]) ).
tcf(c_65063,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12))))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_12766]) ).
tcf(c_65064,plain,
( ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK9))))) = apply(sK1,sK5(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_12766]) ).
tcf(c_65065,plain,
( ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK9))))) = apply(sK1,sK14(sK1,relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_12766]) ).
tcf(c_65066,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1)))))) = apply(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_36111,c_12766]) ).
tcf(c_65529,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_13472]) ).
tcf(c_65533,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_55855,c_13472]) ).
tcf(c_65534,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4726,c_13472]) ).
tcf(c_65537,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56725,c_13472]) ).
tcf(c_65538,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4791,c_13472]) ).
tcf(c_65541,plain,
! [X0: $i] :
( element(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12637,c_13472]) ).
tcf(c_65542,plain,
( element(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5251,c_13472]) ).
tcf(c_65543,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12634,c_13472]) ).
tcf(c_65545,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7241,c_13472]) ).
tcf(c_65546,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK15(sK1,sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7060,c_13472]) ).
tcf(c_65547,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7472,c_13472]) ).
tcf(c_65548,plain,
( element(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6420,c_13472]) ).
tcf(c_65549,plain,
( element(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6421,c_13472]) ).
tcf(c_65557,plain,
! [X0: $i] :
( element(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_58270,c_13472]) ).
tcf(c_65558,plain,
! [X0: $i] :
( element(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59117,c_13472]) ).
tcf(c_65559,plain,
( element(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8770,c_13472]) ).
tcf(c_65560,plain,
( element(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8771,c_13472]) ).
tcf(c_65561,plain,
( element(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8797,c_13472]) ).
tcf(c_65562,plain,
( element(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8798,c_13472]) ).
tcf(c_65563,plain,
( element(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10032,c_13472]) ).
tcf(c_65564,plain,
( element(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10033,c_13472]) ).
tcf(c_65604,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65529,c_65,c_64]) ).
tcf(c_65899,plain,
! [X0: $i] :
( empty(relation_dom(sK2))
| in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_65604,c_68]) ).
tcf(c_65915,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_55855,c_13473]) ).
tcf(c_65919,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56725,c_13473]) ).
tcf(c_65923,plain,
! [X0: $i] :
( in(sK6(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12637,c_13473]) ).
tcf(c_65924,plain,
( in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5251,c_13473]) ).
tcf(c_65925,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12634,c_13473]) ).
tcf(c_65927,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7241,c_13473]) ).
tcf(c_65928,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK15(sK1,sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7060,c_13473]) ).
tcf(c_65929,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7472,c_13473]) ).
tcf(c_65930,plain,
( in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6420,c_13473]) ).
tcf(c_65931,plain,
( in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6421,c_13473]) ).
tcf(c_65939,plain,
! [X0: $i] :
( in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_58270,c_13473]) ).
tcf(c_65940,plain,
! [X0: $i] :
( in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59117,c_13473]) ).
tcf(c_65941,plain,
( in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8770,c_13473]) ).
tcf(c_65942,plain,
( in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8771,c_13473]) ).
tcf(c_65943,plain,
( in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8797,c_13473]) ).
tcf(c_65944,plain,
( in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8798,c_13473]) ).
tcf(c_65945,plain,
( in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10032,c_13473]) ).
tcf(c_65946,plain,
( in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10033,c_13473]) ).
tcf(c_66087,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),sK15(sK1,sK13(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_13387,c_87]) ).
tcf(c_66088,plain,
( in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13387,c_13473]) ).
tcf(c_66089,plain,
( element(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13387,c_13472]) ).
tcf(c_66090,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_13387,c_34564]) ).
tcf(c_66091,plain,
( element(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13387,c_34565]) ).
tcf(c_66092,plain,
( in(sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13387,c_34571]) ).
tcf(c_66093,plain,
( in(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13387,c_34529]) ).
tcf(c_66097,plain,
( in(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13387,c_4623]) ).
tcf(c_66098,plain,
( in(ordered_pair(sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13387,c_62592]) ).
tcf(c_66099,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13387,c_13383]) ).
tcf(c_66131,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),sK15(sK1,sK13(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_66087,c_4030]) ).
tcf(c_66132,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),sK15(sK1,sK13(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66131,c_987,c_3611]) ).
tcf(c_66181,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34273]) ).
tcf(c_66182,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34273]) ).
tcf(c_66183,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34273]) ).
tcf(c_66184,plain,
relation_dom(sK20(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34273]) ).
tcf(c_66185,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34273]) ).
tcf(c_66186,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34273]) ).
tcf(c_66202,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34274]) ).
tcf(c_66203,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34274]) ).
tcf(c_66204,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34274]) ).
tcf(c_66205,plain,
relation_dom(sK20(powerset(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34274]) ).
tcf(c_66206,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34274]) ).
tcf(c_66207,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34274]) ).
tcf(c_66223,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_34275]) ).
tcf(c_66224,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_34275]) ).
tcf(c_66225,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_34275]) ).
tcf(c_66226,plain,
relation_dom(sK20(powerset(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_34275]) ).
tcf(c_66227,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_34275]) ).
tcf(c_66228,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_34275]) ).
tcf(c_66244,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_39385]) ).
tcf(c_66245,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_39385]) ).
tcf(c_66246,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_39385]) ).
tcf(c_66247,plain,
sK20(sK19(powerset(relation_dom(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_39385]) ).
tcf(c_66248,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_39385]) ).
tcf(c_66249,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_39385]) ).
tcf(c_66271,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_39386]) ).
tcf(c_66272,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_39386]) ).
tcf(c_66273,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_39386]) ).
tcf(c_66274,plain,
sK20(sK19(powerset(relation_rng(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_39386]) ).
tcf(c_66275,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_39386]) ).
tcf(c_66276,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_39386]) ).
tcf(c_66311,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_39387]) ).
tcf(c_66312,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_39387]) ).
tcf(c_66313,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_39387]) ).
tcf(c_66314,plain,
sK20(sK19(powerset(relation_inverse(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_39387]) ).
tcf(c_66315,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_39387]) ).
tcf(c_66316,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_39387]) ).
tcf(c_66357,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_13933,c_87]) ).
tcf(c_66358,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13933,c_13473]) ).
tcf(c_66359,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13933,c_13472]) ).
tcf(c_66360,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_13933,c_34564]) ).
tcf(c_66361,plain,
( element(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13933,c_34565]) ).
tcf(c_66362,plain,
( in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13933,c_34571]) ).
tcf(c_66363,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13933,c_34529]) ).
tcf(c_66364,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13933,c_12764]) ).
tcf(c_66365,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13933,c_13488]) ).
tcf(c_66366,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13933,c_12807]) ).
tcf(c_66367,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13933,c_4623]) ).
tcf(c_66368,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13933,c_49959]) ).
tcf(c_66369,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13933,c_12770]) ).
tcf(c_66370,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13933,c_12634]) ).
tcf(c_66433,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_66357,c_4030]) ).
tcf(c_66434,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66433,c_987,c_3611]) ).
tcf(c_66627,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(X0)))) = relation_rng(relation_dom(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3807]) ).
tcf(c_66628,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(X0)))) = relation_rng(relation_dom(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3807]) ).
tcf(c_66629,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(X0)))) = relation_rng(relation_dom(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3807]) ).
tcf(c_66630,plain,
relation_dom(relation_inverse(relation_dom(empty_set))) = relation_rng(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_136,c_3807]) ).
tcf(c_66631,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(X0))))) = relation_rng(relation_dom(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3807]) ).
tcf(c_66632,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = relation_rng(relation_dom(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3807]) ).
tcf(c_66672,plain,
relation_dom(relation_inverse(relation_inverse(sK2))) = relation_rng(relation_inverse(sK2)),
inference(superposition,[status(thm)],[c_61,c_3811]) ).
tcf(c_66674,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(X0)))) = relation_rng(relation_inverse(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_3811]) ).
tcf(c_66675,plain,
relation_dom(relation_inverse(relation_inverse(sK9))) = relation_rng(relation_inverse(sK9)),
inference(superposition,[status(thm)],[c_83,c_3811]) ).
tcf(c_66676,plain,
relation_dom(relation_inverse(relation_inverse(sK10))) = relation_rng(relation_inverse(sK10)),
inference(superposition,[status(thm)],[c_91,c_3811]) ).
tcf(c_66678,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_rng(relation_inverse(relation_inverse(X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_3811]) ).
tcf(c_66679,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_rng(relation_inverse(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_3811]) ).
tcf(c_66680,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(X0)))) = relation_rng(relation_inverse(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_3811]) ).
tcf(c_66681,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(function_inverse(X0)))) = relation_rng(relation_inverse(function_inverse(X0))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_3811]) ).
tcf(c_66682,plain,
relation_dom(relation_inverse(relation_inverse(empty_set))) = relation_rng(relation_inverse(empty_set)),
inference(superposition,[status(thm)],[c_135,c_3811]) ).
tcf(c_66683,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(sK1)))) = relation_rng(relation_inverse(relation_inverse(sK1))),
inference(superposition,[status(thm)],[c_3611,c_3811]) ).
tcf(c_66684,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(sK12)))) = relation_rng(relation_inverse(relation_inverse(sK12))),
inference(superposition,[status(thm)],[c_3610,c_3811]) ).
tcf(c_66685,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0))))) = relation_rng(relation_inverse(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_3811]) ).
tcf(c_66686,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = relation_rng(relation_inverse(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37373,c_3811]) ).
tcf(c_66722,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(X0)))) = relation_rng(relation_rng(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3813]) ).
tcf(c_66723,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(X0)))) = relation_rng(relation_rng(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3813]) ).
tcf(c_66724,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(X0)))) = relation_rng(relation_rng(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3813]) ).
tcf(c_66725,plain,
relation_dom(relation_inverse(relation_rng(empty_set))) = relation_rng(relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_136,c_3813]) ).
tcf(c_66726,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(X0))))) = relation_rng(relation_rng(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3813]) ).
tcf(c_66727,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = relation_rng(relation_rng(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3813]) ).
tcf(c_66752,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK13(sK2,X0)) ),
inference(superposition,[status(thm)],[c_19954,c_70]) ).
tcf(c_66753,plain,
! [X0: $i] :
( element(sK13(sK2,X0),relation_rng(sK2))
| ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19954,c_69]) ).
tcf(c_66755,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK13(sK2,X0))) = sK13(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_19954,c_43161]) ).
tcf(c_66757,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_19954,c_43165]) ).
tcf(c_66785,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),sK6(sK2,X0)) ),
inference(superposition,[status(thm)],[c_20113,c_70]) ).
tcf(c_66786,plain,
! [X0: $i] :
( element(sK6(sK2,X0),relation_rng(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20113,c_69]) ).
tcf(c_66788,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK6(sK2,X0))) = sK6(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_20113,c_43161]) ).
tcf(c_66819,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_13935,c_87]) ).
tcf(c_66820,plain,
( in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13935,c_13473]) ).
tcf(c_66821,plain,
( element(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13935,c_13472]) ).
tcf(c_66822,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_13935,c_34564]) ).
tcf(c_66823,plain,
( element(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13935,c_34565]) ).
tcf(c_66824,plain,
( in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13935,c_34571]) ).
tcf(c_66825,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13935,c_34529]) ).
tcf(c_66826,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13935,c_12764]) ).
tcf(c_66827,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13935,c_13488]) ).
tcf(c_66828,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13935,c_12807]) ).
tcf(c_66829,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13935,c_4623]) ).
tcf(c_66830,plain,
( in(ordered_pair(sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13935,c_49959]) ).
tcf(c_66831,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK15(sK1,sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13935,c_12770]) ).
tcf(c_66832,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( sK15(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13935,c_12634]) ).
tcf(c_66895,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_66819,c_4030]) ).
tcf(c_66896,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_66895,c_987,c_3611]) ).
tcf(c_66947,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(X0)))) = relation_dom(relation_dom(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3847]) ).
tcf(c_66948,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(X0)))) = relation_dom(relation_dom(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3847]) ).
tcf(c_66949,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(X0)))) = relation_dom(relation_dom(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3847]) ).
tcf(c_66950,plain,
relation_rng(relation_inverse(relation_dom(empty_set))) = relation_dom(relation_dom(empty_set)),
inference(superposition,[status(thm)],[c_136,c_3847]) ).
tcf(c_66951,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(X0))))) = relation_dom(relation_dom(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3847]) ).
tcf(c_66952,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))) = relation_dom(relation_dom(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3847]) ).
tcf(c_67166,plain,
relation_rng(relation_inverse(relation_inverse(sK2))) = relation_dom(relation_inverse(sK2)),
inference(superposition,[status(thm)],[c_61,c_3851]) ).
tcf(c_67168,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(X0)))) = relation_dom(relation_inverse(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74,c_3851]) ).
tcf(c_67169,plain,
relation_rng(relation_inverse(relation_inverse(sK9))) = relation_dom(relation_inverse(sK9)),
inference(superposition,[status(thm)],[c_83,c_3851]) ).
tcf(c_67170,plain,
relation_rng(relation_inverse(relation_inverse(sK10))) = relation_dom(relation_inverse(sK10)),
inference(superposition,[status(thm)],[c_91,c_3851]) ).
tcf(c_67172,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_dom(relation_inverse(relation_inverse(X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_123,c_3851]) ).
tcf(c_67173,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))) = relation_dom(relation_inverse(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_122,c_3851]) ).
tcf(c_67174,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(X0)))) = relation_dom(relation_inverse(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_102,c_3851]) ).
tcf(c_67175,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(function_inverse(X0)))) = relation_dom(relation_inverse(function_inverse(X0))) )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_108,c_3851]) ).
tcf(c_67176,plain,
relation_rng(relation_inverse(relation_inverse(empty_set))) = relation_dom(relation_inverse(empty_set)),
inference(superposition,[status(thm)],[c_135,c_3851]) ).
tcf(c_67177,plain,
relation_rng(relation_inverse(relation_inverse(relation_inverse(sK1)))) = relation_dom(relation_inverse(relation_inverse(sK1))),
inference(superposition,[status(thm)],[c_3611,c_3851]) ).
tcf(c_67178,plain,
relation_rng(relation_inverse(relation_inverse(relation_inverse(sK12)))) = relation_dom(relation_inverse(relation_inverse(sK12))),
inference(superposition,[status(thm)],[c_3610,c_3851]) ).
tcf(c_67179,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0))))) = relation_dom(relation_inverse(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_12151,c_3851]) ).
tcf(c_67180,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))) = relation_dom(relation_inverse(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_37373,c_3851]) ).
tcf(c_67216,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(X0)))) = relation_dom(relation_rng(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_3853]) ).
tcf(c_67217,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(X0)))) = relation_dom(relation_rng(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_3853]) ).
tcf(c_67218,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(X0)))) = relation_dom(relation_rng(relation_inverse(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_3853]) ).
tcf(c_67219,plain,
relation_rng(relation_inverse(relation_rng(empty_set))) = relation_dom(relation_rng(empty_set)),
inference(superposition,[status(thm)],[c_136,c_3853]) ).
tcf(c_67220,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(X0))))) = relation_dom(relation_rng(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_3853]) ).
tcf(c_67221,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))) = relation_dom(relation_rng(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_3853]) ).
tcf(c_67263,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK12),X0),sK5(relation_inverse(sK12),X0)),sK12)
| ( relation_dom(relation_inverse(sK12)) = X0 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_3977]) ).
tcf(c_67264,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK12),X0),X0),sK12)
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_dom(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_79,c_3977]) ).
tcf(c_67265,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK12),X0),X0),sK12)
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_dom(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_87,c_3977]) ).
tcf(c_67266,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK12),X0),sK14(relation_inverse(sK12),X0)),sK12)
| ( relation_rng(relation_inverse(sK12)) = X0 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_3977]) ).
tcf(c_67267,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK12),X0)),sK12)
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_rng(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_107,c_3977]) ).
tcf(c_67268,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0)
| ( relation_inverse(relation_inverse(sK12)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_3977]) ).
tcf(c_67269,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_inverse(sK12)),sK21(X0,relation_inverse(sK12))),sK12)
| in(ordered_pair(sK22(X0,relation_inverse(sK12)),sK21(X0,relation_inverse(sK12))),X0)
| ( relation_inverse(X0) = relation_inverse(sK12) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_3977]) ).
tcf(c_67271,plain,
! [X0: $i] :
( in(ordered_pair(sK24(X0,relation_inverse(sK12)),sK23(X0,relation_inverse(sK12))),sK12)
| in(ordered_pair(sK23(X0,relation_inverse(sK12)),sK24(X0,relation_inverse(sK12))),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_3977]) ).
tcf(c_67272,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(sK12),X0),sK23(relation_inverse(sK12),X0)),sK12)
| in(ordered_pair(sK23(relation_inverse(sK12),X0),sK24(relation_inverse(sK12),X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_3977]) ).
tcf(c_67273,plain,
( in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_3977]) ).
tcf(c_67274,plain,
( in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK12),sK1)) = sK23(relation_inverse(sK12),sK1) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_3977]) ).
tcf(c_67275,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_3977]) ).
tcf(c_67276,plain,
( in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_3977]) ).
tcf(c_67277,plain,
( in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK12))) = sK23(sK1,relation_inverse(sK12)) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_3977]) ).
tcf(c_67278,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_3977]) ).
tcf(c_67279,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_3977]) ).
tcf(c_67280,plain,
( in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(sK12),sK1)) = sK21(relation_inverse(sK12),sK1) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_3977]) ).
tcf(c_67281,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_3977]) ).
tcf(c_67282,plain,
( in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_3977]) ).
tcf(c_67283,plain,
( in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_inverse(sK12))) = sK22(sK1,relation_inverse(sK12)) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_3977]) ).
tcf(c_67284,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_3977]) ).
tcf(c_67285,plain,
( in(sK23(sK2,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK12)),sK23(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_3977]) ).
tcf(c_67286,plain,
( in(sK24(sK2,relation_inverse(sK12)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK12)),sK23(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_3977]) ).
tcf(c_67287,plain,
( in(sK22(sK2,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK12)),sK21(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK2) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_3977]) ).
tcf(c_67288,plain,
( in(sK21(sK2,relation_inverse(sK12)),relation_rng(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK12)),sK21(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK2) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_3977]) ).
tcf(c_67289,plain,
( in(sK21(relation_inverse(sK12),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(relation_inverse(sK12)) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_3977]) ).
tcf(c_67290,plain,
( in(sK22(relation_inverse(sK12),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(relation_inverse(sK12)) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_3977]) ).
tcf(c_67291,plain,
( in(sK23(relation_inverse(sK12),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK2),sK23(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_3977]) ).
tcf(c_67292,plain,
( in(sK24(relation_inverse(sK12),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK2),sK23(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_3977]) ).
tcf(c_67293,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK12),X0)),sK12)
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67267,c_3820]) ).
tcf(c_67294,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(relation_inverse(sK12),X0)),sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67293,c_3610]) ).
tcf(c_67297,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK12),X0),X0),sK12)
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67264,c_3810]) ).
tcf(c_67298,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK12),X0),X0),sK12)
| ~ in(X0,relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67297,c_3610]) ).
tcf(c_67301,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK12),X0),X0),sK12)
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67265,c_3810]) ).
tcf(c_67302,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK12),X0),X0),sK12)
| ~ in(X0,relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67301,c_1001,c_3610]) ).
tcf(c_67305,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67278,c_3610]) ).
tcf(c_67309,plain,
( in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67276,c_3610]) ).
tcf(c_67313,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67275,c_3610]) ).
tcf(c_67317,plain,
( in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67273,c_3610]) ).
tcf(c_67321,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK12),X0),sK14(relation_inverse(sK12),X0)),sK12)
| ( relation_dom(sK12) = X0 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67266,c_3820]) ).
tcf(c_67322,plain,
! [X0: $i] :
( in(sK13(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK13(relation_inverse(sK12),X0),sK14(relation_inverse(sK12),X0)),sK12)
| ( relation_dom(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67321,c_3610]) ).
tcf(c_67326,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK12),X0),sK5(relation_inverse(sK12),X0)),sK12)
| ( relation_rng(sK12) = X0 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67263,c_3810]) ).
tcf(c_67327,plain,
! [X0: $i] :
( in(sK5(relation_inverse(sK12),X0),X0)
| in(ordered_pair(sK6(relation_inverse(sK12),X0),sK5(relation_inverse(sK12),X0)),sK12)
| ( relation_rng(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67326,c_3610]) ).
tcf(c_67331,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67284,c_3610]) ).
tcf(c_67335,plain,
( in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67282,c_3610]) ).
tcf(c_67339,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67281,c_3629]) ).
tcf(c_67340,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67339,c_3610]) ).
tcf(c_67344,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67279,c_3629]) ).
tcf(c_67345,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67344,c_3610]) ).
tcf(c_67349,plain,
( in(sK24(relation_inverse(sK12),sK2),relation_rng(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK2),sK23(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67292,c_3610]) ).
tcf(c_67354,plain,
( in(sK23(relation_inverse(sK12),sK2),relation_dom(sK2))
| in(ordered_pair(sK24(relation_inverse(sK12),sK2),sK23(relation_inverse(sK12),sK2)),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67291,c_3610]) ).
tcf(c_67359,plain,
( in(sK24(sK2,relation_inverse(sK12)),relation_rng(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK12)),sK23(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67286,c_3610]) ).
tcf(c_67364,plain,
( in(sK23(sK2,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK24(sK2,relation_inverse(sK12)),sK23(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67285,c_3610]) ).
tcf(c_67369,plain,
( in(sK22(relation_inverse(sK12),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_67290,c_3629]) ).
tcf(c_67370,plain,
( in(sK22(relation_inverse(sK12),sK2),relation_rng(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67369,c_3610]) ).
tcf(c_67375,plain,
( in(sK21(relation_inverse(sK12),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_67289,c_3629]) ).
tcf(c_67376,plain,
( in(sK21(relation_inverse(sK12),sK2),relation_dom(sK2))
| in(ordered_pair(sK21(relation_inverse(sK12),sK2),sK22(relation_inverse(sK12),sK2)),sK12)
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67375,c_3610]) ).
tcf(c_67381,plain,
( in(sK21(sK2,relation_inverse(sK12)),relation_rng(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK12)),sK21(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK2) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67288,c_3610]) ).
tcf(c_67386,plain,
( in(sK22(sK2,relation_inverse(sK12)),relation_dom(sK2))
| in(ordered_pair(sK22(sK2,relation_inverse(sK12)),sK21(sK2,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK2) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67287,c_3610]) ).
tcf(c_67391,plain,
( in(ordered_pair(sK24(sK1,relation_inverse(sK12)),sK23(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK12))) = sK23(sK1,relation_inverse(sK12)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67277,c_3610]) ).
tcf(c_67395,plain,
( in(ordered_pair(sK24(relation_inverse(sK12),sK1),sK23(relation_inverse(sK12),sK1)),sK12)
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK12),sK1)) = sK23(relation_inverse(sK12),sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67274,c_3610]) ).
tcf(c_67399,plain,
( in(ordered_pair(sK22(sK1,relation_inverse(sK12)),sK21(sK1,relation_inverse(sK12))),sK12)
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_inverse(sK12))) = sK22(sK1,relation_inverse(sK12)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67283,c_3610]) ).
tcf(c_67403,plain,
( in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(sK12),sK1)) = sK21(relation_inverse(sK12),sK1) )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67280,c_3629]) ).
tcf(c_67404,plain,
( in(ordered_pair(sK21(relation_inverse(sK12),sK1),sK22(relation_inverse(sK12),sK1)),sK12)
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK22(relation_inverse(sK12),sK1)) = sK21(relation_inverse(sK12),sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67403,c_3610]) ).
tcf(c_67408,plain,
! [X0: $i] :
( in(ordered_pair(sK24(relation_inverse(sK12),X0),sK23(relation_inverse(sK12),X0)),sK12)
| in(ordered_pair(sK23(relation_inverse(sK12),X0),sK24(relation_inverse(sK12),X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67272,c_3610]) ).
tcf(c_67413,plain,
! [X0: $i] :
( in(ordered_pair(sK24(X0,relation_inverse(sK12)),sK23(X0,relation_inverse(sK12))),sK12)
| in(ordered_pair(sK23(X0,relation_inverse(sK12)),sK24(X0,relation_inverse(sK12))),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67271,c_3610]) ).
tcf(c_67418,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_inverse(sK12)),sK21(X0,relation_inverse(sK12))),sK12)
| in(ordered_pair(sK22(X0,relation_inverse(sK12)),sK21(X0,relation_inverse(sK12))),X0)
| ( relation_inverse(X0) = relation_inverse(sK12) )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67269,c_3610]) ).
tcf(c_67423,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0)
| ( X0 = sK12 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_67268,c_3629]) ).
tcf(c_67424,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0)
| ( X0 = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67423,c_3610]) ).
tcf(c_67433,plain,
! [X0: $i,X1: $i] :
( ~ in(ordered_pair(X1,X0),sK12)
| ~ in(relation_inverse(sK12),ordered_pair(X0,X1)) ),
inference(superposition,[status(thm)],[c_3980,c_70]) ).
tcf(c_67434,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X1,X0),relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_69]) ).
tcf(c_67435,plain,
! [X0: $i,X1: $i] :
( ~ empty(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_67]) ).
tcf(c_67436,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK12)) = X1 )
| ~ relation(relation_inverse(sK12))
| ~ in(sK5(relation_inverse(sK12),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK12),X1)),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_76]) ).
tcf(c_67437,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_rng(relation_inverse(sK12)))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_106]) ).
tcf(c_67438,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_dom(relation_inverse(sK12)))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_78]) ).
tcf(c_67439,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK12),X1) = X0 )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_197]) ).
tcf(c_67440,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK12)) = X0 )
| ~ relation(relation_inverse(sK12))
| ~ in(sK13(relation_inverse(sK12),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK12),X0),X1),sK12) ),
inference(superposition,[status(thm)],[c_3980,c_104]) ).
tcf(c_67441,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK12)) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0) ),
inference(superposition,[status(thm)],[c_3980,c_124]) ).
tcf(c_67443,plain,
! [X0: $i] :
( ( relation_inverse(sK12) = X0 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(sK24(X0,relation_inverse(sK12)),sK23(X0,relation_inverse(sK12))),sK12)
| ~ in(ordered_pair(sK23(X0,relation_inverse(sK12)),sK24(X0,relation_inverse(sK12))),X0) ),
inference(superposition,[status(thm)],[c_3980,c_129]) ).
tcf(c_67451,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(light_normalisation,[status(thm)],[c_67438,c_3810]) ).
tcf(c_67452,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67451,c_3610]) ).
tcf(c_67455,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(light_normalisation,[status(thm)],[c_67437,c_3820]) ).
tcf(c_67456,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(sK12))
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67455,c_3610]) ).
tcf(c_67459,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK12),X1) = X0 )
| ~ in(ordered_pair(X0,X1),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67439,c_1001,c_3610]) ).
tcf(c_67462,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK12) = X0 )
| ~ relation(relation_inverse(sK12))
| ~ in(sK13(relation_inverse(sK12),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK12),X0),X1),sK12) ),
inference(light_normalisation,[status(thm)],[c_67440,c_3820]) ).
tcf(c_67463,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK12) = X0 )
| ~ in(sK13(relation_inverse(sK12),X0),X0)
| ~ in(ordered_pair(sK13(relation_inverse(sK12),X0),X1),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67462,c_3610]) ).
tcf(c_67467,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK12) = X1 )
| ~ relation(relation_inverse(sK12))
| ~ in(sK5(relation_inverse(sK12),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK12),X1)),sK12) ),
inference(light_normalisation,[status(thm)],[c_67436,c_3810]) ).
tcf(c_67468,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK12) = X1 )
| ~ in(sK5(relation_inverse(sK12),X1),X1)
| ~ in(ordered_pair(X0,sK5(relation_inverse(sK12),X1)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67467,c_3610]) ).
tcf(c_67472,plain,
! [X0: $i] :
( ( relation_inverse(sK12) = X0 )
| ~ relation(X0)
| ~ in(ordered_pair(sK24(X0,relation_inverse(sK12)),sK23(X0,relation_inverse(sK12))),sK12)
| ~ in(ordered_pair(sK23(X0,relation_inverse(sK12)),sK24(X0,relation_inverse(sK12))),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67443,c_3610]) ).
tcf(c_67477,plain,
! [X0: $i] :
( ( X0 = sK12 )
| ~ relation(X0)
| ~ relation(relation_inverse(sK12))
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0) ),
inference(light_normalisation,[status(thm)],[c_67441,c_3629]) ).
tcf(c_67478,plain,
! [X0: $i] :
( ( X0 = sK12 )
| ~ relation(X0)
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),sK12)
| ~ in(ordered_pair(sK21(relation_inverse(sK12),X0),sK22(relation_inverse(sK12),X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67477,c_3610]) ).
tcf(c_67487,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| ( relation_dom(sK12) = X0 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_67435]) ).
tcf(c_67490,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| ( relation_rng(sK12) = X0 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_67435]) ).
tcf(c_67492,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(sK12)
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_67435]) ).
tcf(c_67493,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(sK12)
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_67435]) ).
tcf(c_67494,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_67435]) ).
tcf(c_67495,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_67435]) ).
tcf(c_67496,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_67435]) ).
tcf(c_67497,plain,
( ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_67435]) ).
tcf(c_67498,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_67435]) ).
tcf(c_67499,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_67435]) ).
tcf(c_67500,plain,
( ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_67435]) ).
tcf(c_67501,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_67435]) ).
tcf(c_67502,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_67435]) ).
tcf(c_67503,plain,
( ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_67435]) ).
tcf(c_67504,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_67435]) ).
tcf(c_67505,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_67435]) ).
tcf(c_67506,plain,
( ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_67435]) ).
tcf(c_67507,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_67435]) ).
tcf(c_67508,plain,
( in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_67435]) ).
tcf(c_67509,plain,
( in(sK24(sK2,sK12),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_67435]) ).
tcf(c_67510,plain,
( in(sK22(sK2,sK12),relation_dom(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_67435]) ).
tcf(c_67511,plain,
( in(sK21(sK2,sK12),relation_rng(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_67435]) ).
tcf(c_67512,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_67435]) ).
tcf(c_67513,plain,
( in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_67435]) ).
tcf(c_67514,plain,
( in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_67435]) ).
tcf(c_67515,plain,
( in(sK24(sK12,sK2),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_67435]) ).
tcf(c_67516,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67501,c_95]) ).
tcf(c_67520,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67499,c_95]) ).
tcf(c_67524,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67498,c_95]) ).
tcf(c_67528,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67496,c_95]) ).
tcf(c_67532,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| ( relation_rng(sK12) = X0 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67490,c_95]) ).
tcf(c_67536,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| ( relation_dom(sK12) = X0 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67487,c_95]) ).
tcf(c_67540,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67507,c_95]) ).
tcf(c_67544,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67505,c_95]) ).
tcf(c_67548,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67504,c_95]) ).
tcf(c_67552,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67502,c_95]) ).
tcf(c_67556,plain,
( in(sK24(sK12,sK2),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67515,c_95]) ).
tcf(c_67561,plain,
( in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67514,c_95]) ).
tcf(c_67566,plain,
( in(sK24(sK2,sK12),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67509,c_95]) ).
tcf(c_67571,plain,
( in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67508,c_95]) ).
tcf(c_67576,plain,
( in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67513,c_95]) ).
tcf(c_67581,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67512,c_95]) ).
tcf(c_67586,plain,
( in(sK21(sK2,sK12),relation_rng(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67511,c_95]) ).
tcf(c_67591,plain,
( in(sK22(sK2,sK12),relation_dom(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ empty(relation_inverse(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67510,c_95]) ).
tcf(c_67596,plain,
( ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67500,c_95]) ).
tcf(c_67600,plain,
( ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67497,c_95]) ).
tcf(c_67604,plain,
( ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67506,c_95]) ).
tcf(c_67608,plain,
( ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) )
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67503,c_95]) ).
tcf(c_67612,plain,
! [X0: $i] :
( in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67495,c_95]) ).
tcf(c_67617,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67494,c_95]) ).
tcf(c_67622,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67493,c_95]) ).
tcf(c_67627,plain,
! [X0: $i] :
( in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67492,c_95]) ).
tcf(c_67796,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| in(sK6(sK12,X0),relation_rng(sK12))
| ( relation_dom(sK12) = X0 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_77,c_67452]) ).
tcf(c_67797,plain,
! [X0: $i] :
( in(sK7(sK12,X0),relation_rng(sK12))
| ~ relation(sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_79,c_67452]) ).
tcf(c_67798,plain,
! [X0: $i] :
( in(apply(sK12,X0),relation_rng(sK12))
| ~ function(sK12)
| ~ relation(sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_87,c_67452]) ).
tcf(c_67799,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| in(sK13(sK12,X0),relation_rng(sK12))
| ( relation_rng(sK12) = X0 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_105,c_67452]) ).
tcf(c_67801,plain,
! [X0: $i] :
( in(sK21(sK12,X0),relation_rng(sK12))
| in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67452]) ).
tcf(c_67802,plain,
! [X0: $i] :
( in(sK22(X0,sK12),relation_rng(sK12))
| in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67452]) ).
tcf(c_67803,plain,
! [X0: $i] :
( in(sK24(X0,sK12),relation_rng(sK12))
| in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67452]) ).
tcf(c_67804,plain,
! [X0: $i] :
( in(sK24(sK12,X0),relation_rng(sK12))
| in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67452]) ).
tcf(c_67805,plain,
( in(sK24(sK12,sK1),relation_rng(sK12))
| in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8327,c_67452]) ).
tcf(c_67806,plain,
( in(sK24(sK12,sK1),relation_rng(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5709,c_67452]) ).
tcf(c_67807,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| in(sK24(sK12,sK1),relation_rng(sK12))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5669,c_67452]) ).
tcf(c_67808,plain,
( in(sK24(sK1,sK12),relation_rng(sK12))
| in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8322,c_67452]) ).
tcf(c_67809,plain,
( in(sK24(sK1,sK12),relation_rng(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5704,c_67452]) ).
tcf(c_67810,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| in(sK24(sK1,sK12),relation_rng(sK12))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5654,c_67452]) ).
tcf(c_67811,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| in(sK21(sK12,sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8332,c_67452]) ).
tcf(c_67812,plain,
( in(sK21(sK12,sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5969,c_67452]) ).
tcf(c_67813,plain,
( in(sK21(sK12,sK1),relation_rng(sK12))
| in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5929,c_67452]) ).
tcf(c_67814,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8337,c_67452]) ).
tcf(c_67815,plain,
( in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5964,c_67452]) ).
tcf(c_67816,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5914,c_67452]) ).
tcf(c_67817,plain,
( in(sK24(sK2,sK12),relation_rng(sK12))
| in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_67452]) ).
tcf(c_67818,plain,
( in(sK24(sK2,sK12),relation_rng(sK12))
| in(sK24(sK2,sK12),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_67452]) ).
tcf(c_67819,plain,
( in(sK22(sK2,sK12),relation_dom(sK2))
| in(sK22(sK2,sK12),relation_rng(sK12))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_67452]) ).
tcf(c_67820,plain,
( in(sK21(sK2,sK12),relation_rng(sK2))
| in(sK22(sK2,sK12),relation_rng(sK12))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_67452]) ).
tcf(c_67821,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| in(sK21(sK12,sK2),relation_rng(sK12))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_67452]) ).
tcf(c_67822,plain,
( in(sK21(sK12,sK2),relation_rng(sK12))
| in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_67452]) ).
tcf(c_67823,plain,
( in(sK24(sK12,sK2),relation_rng(sK12))
| in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_67452]) ).
tcf(c_67824,plain,
( in(sK24(sK12,sK2),relation_rng(sK12))
| in(sK24(sK12,sK2),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_67452]) ).
tcf(c_67825,plain,
! [X0: $i] :
( in(sK7(sK12,X0),relation_rng(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67797,c_95]) ).
tcf(c_67828,plain,
! [X0: $i] :
( in(apply(sK12,X0),relation_rng(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67798,c_96,c_95]) ).
tcf(c_67831,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| in(sK24(sK1,sK12),relation_rng(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67810,c_95]) ).
tcf(c_67835,plain,
( in(sK24(sK1,sK12),relation_rng(sK12))
| in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67808,c_95]) ).
tcf(c_67839,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| in(sK24(sK12,sK1),relation_rng(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67807,c_95]) ).
tcf(c_67843,plain,
( in(sK24(sK12,sK1),relation_rng(sK12))
| in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67805,c_95]) ).
tcf(c_67847,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| in(sK13(sK12,X0),relation_rng(sK12))
| ( relation_rng(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67799,c_95]) ).
tcf(c_67851,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| in(sK6(sK12,X0),relation_rng(sK12))
| ( relation_dom(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67796,c_95]) ).
tcf(c_67855,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67816,c_95]) ).
tcf(c_67859,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67814,c_95]) ).
tcf(c_67863,plain,
( in(sK21(sK12,sK1),relation_rng(sK12))
| in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67813,c_95]) ).
tcf(c_67867,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| in(sK21(sK12,sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67811,c_95]) ).
tcf(c_67871,plain,
( in(sK24(sK12,sK2),relation_rng(sK12))
| in(sK24(sK12,sK2),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67824,c_95]) ).
tcf(c_67876,plain,
( in(sK24(sK12,sK2),relation_rng(sK12))
| in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67823,c_95]) ).
tcf(c_67881,plain,
( in(sK24(sK2,sK12),relation_rng(sK12))
| in(sK24(sK2,sK12),relation_rng(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67818,c_95]) ).
tcf(c_67886,plain,
( in(sK24(sK2,sK12),relation_rng(sK12))
| in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67817,c_95]) ).
tcf(c_67891,plain,
( in(sK21(sK12,sK2),relation_rng(sK12))
| in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67822,c_95]) ).
tcf(c_67896,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| in(sK21(sK12,sK2),relation_rng(sK12))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67821,c_95]) ).
tcf(c_67901,plain,
( in(sK21(sK2,sK12),relation_rng(sK2))
| in(sK22(sK2,sK12),relation_rng(sK12))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67820,c_95]) ).
tcf(c_67906,plain,
( in(sK22(sK2,sK12),relation_dom(sK2))
| in(sK22(sK2,sK12),relation_rng(sK12))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67819,c_95]) ).
tcf(c_67911,plain,
( in(sK24(sK1,sK12),relation_rng(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67809,c_95]) ).
tcf(c_67915,plain,
( in(sK24(sK12,sK1),relation_rng(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67806,c_95]) ).
tcf(c_67919,plain,
( in(sK22(sK1,sK12),relation_rng(sK12))
| ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67815,c_95]) ).
tcf(c_67923,plain,
( in(sK21(sK12,sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67812,c_95]) ).
tcf(c_67927,plain,
! [X0: $i] :
( in(sK24(sK12,X0),relation_rng(sK12))
| in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67804,c_95]) ).
tcf(c_67932,plain,
! [X0: $i] :
( in(sK24(X0,sK12),relation_rng(sK12))
| in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67803,c_95]) ).
tcf(c_67937,plain,
! [X0: $i] :
( in(sK22(X0,sK12),relation_rng(sK12))
| in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67802,c_95]) ).
tcf(c_67942,plain,
! [X0: $i] :
( in(sK21(sK12,X0),relation_rng(sK12))
| in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67801,c_95]) ).
tcf(c_67959,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| in(sK5(sK12,X0),relation_dom(sK12))
| ( relation_dom(sK12) = X0 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_77,c_67456]) ).
tcf(c_67962,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| in(sK14(sK12,X0),relation_dom(sK12))
| ( relation_rng(sK12) = X0 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_105,c_67456]) ).
tcf(c_67963,plain,
! [X0: $i] :
( in(sK15(sK12,X0),relation_dom(sK12))
| ~ relation(sK12)
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_107,c_67456]) ).
tcf(c_67964,plain,
! [X0: $i] :
( in(sK22(sK12,X0),relation_dom(sK12))
| in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67456]) ).
tcf(c_67965,plain,
! [X0: $i] :
( in(sK21(X0,sK12),relation_dom(sK12))
| in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_125,c_67456]) ).
tcf(c_67966,plain,
! [X0: $i] :
( in(sK23(X0,sK12),relation_dom(sK12))
| in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67456]) ).
tcf(c_67967,plain,
! [X0: $i] :
( in(sK23(sK12,X0),relation_dom(sK12))
| in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(sK12)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_130,c_67456]) ).
tcf(c_67968,plain,
( in(sK23(sK12,sK1),relation_dom(sK12))
| in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8327,c_67456]) ).
tcf(c_67969,plain,
( in(sK23(sK12,sK1),relation_dom(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5709,c_67456]) ).
tcf(c_67970,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| in(sK23(sK12,sK1),relation_dom(sK12))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5669,c_67456]) ).
tcf(c_67971,plain,
( in(sK23(sK1,sK12),relation_dom(sK12))
| in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8322,c_67456]) ).
tcf(c_67972,plain,
( in(sK23(sK1,sK12),relation_dom(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5704,c_67456]) ).
tcf(c_67973,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| in(sK23(sK1,sK12),relation_dom(sK12))
| ( sK1 = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5654,c_67456]) ).
tcf(c_67974,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| in(sK22(sK12,sK1),relation_dom(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8332,c_67456]) ).
tcf(c_67975,plain,
( in(sK22(sK12,sK1),relation_dom(sK12))
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5969,c_67456]) ).
tcf(c_67976,plain,
( in(sK22(sK12,sK1),relation_dom(sK12))
| in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5929,c_67456]) ).
tcf(c_67977,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_8337,c_67456]) ).
tcf(c_67978,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5964,c_67456]) ).
tcf(c_67979,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_5914,c_67456]) ).
tcf(c_67980,plain,
( in(sK23(sK2,sK12),relation_dom(sK12))
| in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23755,c_67456]) ).
tcf(c_67981,plain,
( in(sK24(sK2,sK12),relation_rng(sK2))
| in(sK23(sK2,sK12),relation_dom(sK12))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18823,c_67456]) ).
tcf(c_67982,plain,
( in(sK21(sK2,sK12),relation_dom(sK12))
| in(sK22(sK2,sK12),relation_dom(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23773,c_67456]) ).
tcf(c_67983,plain,
( in(sK21(sK2,sK12),relation_dom(sK12))
| in(sK21(sK2,sK12),relation_rng(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18841,c_67456]) ).
tcf(c_67984,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| in(sK22(sK12,sK2),relation_dom(sK12))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23767,c_67456]) ).
tcf(c_67985,plain,
( in(sK22(sK12,sK2),relation_dom(sK12))
| in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18835,c_67456]) ).
tcf(c_67986,plain,
( in(sK23(sK12,sK2),relation_dom(sK12))
| in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23761,c_67456]) ).
tcf(c_67987,plain,
( in(sK24(sK12,sK2),relation_rng(sK2))
| in(sK23(sK12,sK2),relation_dom(sK12))
| ( sK2 = sK12 )
| ~ relation(sK12)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18829,c_67456]) ).
tcf(c_67988,plain,
! [X0: $i] :
( in(sK15(sK12,X0),relation_dom(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67963,c_95]) ).
tcf(c_67991,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| in(sK23(sK1,sK12),relation_dom(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67973,c_95]) ).
tcf(c_67995,plain,
( in(sK23(sK1,sK12),relation_dom(sK12))
| in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67971,c_95]) ).
tcf(c_67999,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| in(sK23(sK12,sK1),relation_dom(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67970,c_95]) ).
tcf(c_68003,plain,
( in(sK23(sK12,sK1),relation_dom(sK12))
| in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67968,c_95]) ).
tcf(c_68007,plain,
! [X0: $i] :
( in(sK13(sK12,X0),X0)
| in(sK14(sK12,X0),relation_dom(sK12))
| ( relation_rng(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67962,c_95]) ).
tcf(c_68011,plain,
! [X0: $i] :
( in(sK5(sK12,X0),X0)
| in(sK5(sK12,X0),relation_dom(sK12))
| ( relation_dom(sK12) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67959,c_95]) ).
tcf(c_68015,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67979,c_95]) ).
tcf(c_68019,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67977,c_95]) ).
tcf(c_68023,plain,
( in(sK22(sK12,sK1),relation_dom(sK12))
| in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67976,c_95]) ).
tcf(c_68027,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| in(sK22(sK12,sK1),relation_dom(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67974,c_95]) ).
tcf(c_68031,plain,
( in(sK24(sK12,sK2),relation_rng(sK2))
| in(sK23(sK12,sK2),relation_dom(sK12))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67987,c_95]) ).
tcf(c_68036,plain,
( in(sK23(sK12,sK2),relation_dom(sK12))
| in(sK23(sK12,sK2),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67986,c_95]) ).
tcf(c_68041,plain,
( in(sK24(sK2,sK12),relation_rng(sK2))
| in(sK23(sK2,sK12),relation_dom(sK12))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67981,c_95]) ).
tcf(c_68046,plain,
( in(sK23(sK2,sK12),relation_dom(sK12))
| in(sK23(sK2,sK12),relation_dom(sK2))
| ( sK2 = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67980,c_95]) ).
tcf(c_68051,plain,
( in(sK22(sK12,sK2),relation_dom(sK12))
| in(sK22(sK12,sK2),relation_rng(sK2))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67985,c_95]) ).
tcf(c_68056,plain,
( in(sK21(sK12,sK2),relation_dom(sK2))
| in(sK22(sK12,sK2),relation_dom(sK12))
| ( relation_inverse(sK12) = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67984,c_95]) ).
tcf(c_68061,plain,
( in(sK21(sK2,sK12),relation_dom(sK12))
| in(sK21(sK2,sK12),relation_rng(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67983,c_95]) ).
tcf(c_68066,plain,
( in(sK21(sK2,sK12),relation_dom(sK12))
| in(sK22(sK2,sK12),relation_dom(sK2))
| ( relation_inverse(sK2) = sK12 )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67982,c_95]) ).
tcf(c_68071,plain,
( in(sK23(sK1,sK12),relation_dom(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK12)) = sK23(sK1,sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67972,c_95]) ).
tcf(c_68075,plain,
( in(sK23(sK12,sK1),relation_dom(sK12))
| ( sK1 = sK12 )
| ( apply(relation_inverse(sK1),sK24(sK12,sK1)) = sK23(sK12,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67969,c_95]) ).
tcf(c_68079,plain,
( in(sK21(sK1,sK12),relation_dom(sK12))
| ( relation_inverse(sK1) = sK12 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK12)) = sK22(sK1,sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67978,c_95]) ).
tcf(c_68083,plain,
( in(sK22(sK12,sK1),relation_dom(sK12))
| ( relation_inverse(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK12,sK1)) = sK21(sK12,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67975,c_95]) ).
tcf(c_68087,plain,
! [X0: $i] :
( in(sK23(sK12,X0),relation_dom(sK12))
| in(ordered_pair(sK23(sK12,X0),sK24(sK12,X0)),X0)
| ( X0 = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67967,c_95]) ).
tcf(c_68092,plain,
! [X0: $i] :
( in(sK23(X0,sK12),relation_dom(sK12))
| in(ordered_pair(sK23(X0,sK12),sK24(X0,sK12)),X0)
| ( X0 = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67966,c_95]) ).
tcf(c_68097,plain,
! [X0: $i] :
( in(sK21(X0,sK12),relation_dom(sK12))
| in(ordered_pair(sK22(X0,sK12),sK21(X0,sK12)),X0)
| ( relation_inverse(X0) = sK12 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67965,c_95]) ).
tcf(c_68102,plain,
! [X0: $i] :
( in(sK22(sK12,X0),relation_dom(sK12))
| in(ordered_pair(sK21(sK12,X0),sK22(sK12,X0)),X0)
| ( relation_inverse(sK12) = X0 )
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67964,c_95]) ).
tcf(c_68142,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK14(sK2,X0)) ),
inference(superposition,[status(thm)],[c_24569,c_70]) ).
tcf(c_68143,plain,
! [X0: $i] :
( element(sK14(sK2,X0),relation_dom(sK2))
| ( relation_rng(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_69]) ).
tcf(c_68146,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK14(sK2,X0))) = apply(sK1,sK15(sK1,sK14(sK2,X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_12335]) ).
tcf(c_68147,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK14(sK2,X0)))) = sK15(sK1,sK14(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_8396]) ).
tcf(c_68148,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK14(sK2,X0)))) = sK15(sK1,sK14(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_8395]) ).
tcf(c_68149,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_4044]) ).
tcf(c_68150,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK14(sK2,X0)) = apply(sK2,sK14(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_42224]) ).
tcf(c_68151,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_12701]) ).
tcf(c_68152,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK14(sK2,X0))) = sK14(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_10144]) ).
tcf(c_68153,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK14(sK2,X0)) = sK15(sK1,sK14(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24569,c_4468]) ).
tcf(c_68332,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK5(sK2,X0)) ),
inference(superposition,[status(thm)],[c_24797,c_70]) ).
tcf(c_68333,plain,
! [X0: $i] :
( element(sK5(sK2,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_69]) ).
tcf(c_68336,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK5(sK2,X0))) = apply(sK1,sK15(sK1,sK5(sK2,X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_12335]) ).
tcf(c_68337,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK5(sK2,X0)))) = sK15(sK1,sK5(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_8396]) ).
tcf(c_68338,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK5(sK2,X0)))) = sK15(sK1,sK5(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_8395]) ).
tcf(c_68339,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(sK2,sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_4044]) ).
tcf(c_68340,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( sK15(relation_inverse(sK2),sK5(sK2,X0)) = apply(sK2,sK5(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_42224]) ).
tcf(c_68341,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_12701]) ).
tcf(c_68342,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK2,X0))) = sK5(sK2,X0) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_10144]) ).
tcf(c_68343,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK5(sK2,X0)) = sK15(sK1,sK5(sK2,X0)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_24797,c_4468]) ).
tcf(c_68345,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ in(sK5(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_24797,c_42228]) ).
tcf(c_68469,plain,
! [X0: $i] :
( ~ empty(sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_67825,c_30414]) ).
tcf(c_68470,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK12))
| ~ in(relation_rng(sK12),sK7(sK12,X0)) ),
inference(superposition,[status(thm)],[c_67825,c_70]) ).
tcf(c_68471,plain,
! [X0: $i] :
( element(sK7(sK12,X0),relation_rng(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_67825,c_69]) ).
tcf(c_68472,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_67825,c_67]) ).
tcf(c_68490,plain,
! [X0: $i] :
( ( apply(sK12,X0) = empty_set )
| ~ function(sK12)
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_89,c_68472]) ).
tcf(c_68491,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK12),X0),X0)
| ( relation_dom(relation_dom(sK12)) = X0 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_68472]) ).
tcf(c_68492,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_dom(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_79,c_68472]) ).
tcf(c_68493,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK12))
| ~ function(relation_dom(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_dom(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_87,c_68472]) ).
tcf(c_68494,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK12),X0),X0)
| ( relation_rng(relation_dom(sK12)) = X0 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_68472]) ).
tcf(c_68495,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12))
| ~ in(X0,relation_rng(relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_107,c_68472]) ).
tcf(c_68496,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK12),X0),sK22(relation_dom(sK12),X0)),X0)
| ( relation_inverse(relation_dom(sK12)) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_68472]) ).
tcf(c_68497,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK12)),sK21(X0,relation_dom(sK12))),X0)
| ( relation_inverse(X0) = relation_dom(sK12) )
| ~ relation(X0)
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_68472]) ).
tcf(c_68498,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK12)),sK24(X0,relation_dom(sK12))),X0)
| ( relation_dom(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_68472]) ).
tcf(c_68499,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK12),X0),sK24(relation_dom(sK12),X0)),X0)
| ( relation_dom(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_68472]) ).
tcf(c_68501,plain,
( element(sK5(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8548,c_68472]) ).
tcf(c_68502,plain,
( element(sK6(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_6286,c_68472]) ).
tcf(c_68503,plain,
( in(sK5(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8302,c_68472]) ).
tcf(c_68504,plain,
( in(sK6(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5335,c_68472]) ).
tcf(c_68505,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5141,c_68472]) ).
tcf(c_68506,plain,
( element(sK14(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8430,c_68472]) ).
tcf(c_68507,plain,
( element(sK13(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_6336,c_68472]) ).
tcf(c_68508,plain,
( in(sK14(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8298,c_68472]) ).
tcf(c_68509,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5563,c_68472]) ).
tcf(c_68510,plain,
( in(sK13(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5542,c_68472]) ).
tcf(c_68511,plain,
( in(sK23(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_68472]) ).
tcf(c_68512,plain,
( ( relation_dom(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK12),sK1)) = sK23(relation_dom(sK12),sK1) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_68472]) ).
tcf(c_68513,plain,
( in(sK24(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_68472]) ).
tcf(c_68514,plain,
( in(sK23(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_68472]) ).
tcf(c_68515,plain,
( ( relation_dom(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK12))) = sK23(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_68472]) ).
tcf(c_68516,plain,
( in(sK24(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_68472]) ).
tcf(c_68517,plain,
( in(sK21(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(relation_dom(sK12)) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_68472]) ).
tcf(c_68518,plain,
( ( relation_inverse(relation_dom(sK12)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK12),sK1)) = sK21(relation_dom(sK12),sK1) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_68472]) ).
tcf(c_68519,plain,
( in(sK22(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK1 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_68472]) ).
tcf(c_68520,plain,
( in(sK22(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK12) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_68472]) ).
tcf(c_68521,plain,
( ( relation_dom(sK12) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK12))) = sK22(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_68472]) ).
tcf(c_68522,plain,
( in(sK21(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = relation_inverse(sK1) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_68472]) ).
tcf(c_68523,plain,
( ( relation_dom(sK12) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8158,c_68472]) ).
tcf(c_68525,plain,
( in(sK23(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23755,c_68472]) ).
tcf(c_68526,plain,
( in(sK24(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18823,c_68472]) ).
tcf(c_68527,plain,
( in(sK5(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_68472]) ).
tcf(c_68528,plain,
( in(sK6(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_68472]) ).
tcf(c_68529,plain,
( in(sK14(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_68472]) ).
tcf(c_68530,plain,
( in(sK13(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_68472]) ).
tcf(c_68531,plain,
( in(sK22(sK2,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23773,c_68472]) ).
tcf(c_68532,plain,
( in(sK21(sK2,relation_dom(sK12)),relation_rng(sK2))
| ( relation_dom(sK12) = relation_inverse(sK2) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18841,c_68472]) ).
tcf(c_68533,plain,
( in(sK21(relation_dom(sK12),sK2),relation_dom(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23767,c_68472]) ).
tcf(c_68534,plain,
( in(sK22(relation_dom(sK12),sK2),relation_rng(sK2))
| ( relation_inverse(relation_dom(sK12)) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18835,c_68472]) ).
tcf(c_68535,plain,
( in(sK23(relation_dom(sK12),sK2),relation_dom(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_23761,c_68472]) ).
tcf(c_68536,plain,
( in(sK24(relation_dom(sK12),sK2),relation_rng(sK2))
| ( relation_dom(sK12) = sK2 )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_18829,c_68472]) ).
tcf(c_68537,plain,
( empty(relation_dom(sK12))
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_36111,c_68472]) ).
tcf(c_68548,plain,
! [X0: $i] :
( ( apply(sK12,X0) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68490,c_96,c_95]) ).
tcf(c_68952,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK12))
| ~ in(relation_rng(sK12),apply(sK12,X0)) ),
inference(superposition,[status(thm)],[c_67828,c_70]) ).
tcf(c_68953,plain,
! [X0: $i] :
( element(apply(sK12,X0),relation_rng(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_67828,c_69]) ).
tcf(c_68978,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(relation_dom(sK1),sK5(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_68503,c_70]) ).
tcf(c_68982,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12))))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_12766]) ).
tcf(c_68983,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12))))) = sK7(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_12765]) ).
tcf(c_68984,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12))))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_10203]) ).
tcf(c_68985,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12))))) = sK7(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_10202]) ).
tcf(c_68986,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_6249]) ).
tcf(c_68987,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_5349]) ).
tcf(c_68989,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_dom(sK12))) = apply(sK1,sK5(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_12284]) ).
tcf(c_68990,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_4619]) ).
tcf(c_68991,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_4406]) ).
tcf(c_68992,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(sK5(sK1,relation_dom(sK12)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_12287]) ).
tcf(c_69212,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(relation_dom(sK2),sK6(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_68504,c_70]) ).
tcf(c_69216,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_dom(sK12)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_12335]) ).
tcf(c_69217,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12))))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_8396]) ).
tcf(c_69218,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_dom(sK12))))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_8395]) ).
tcf(c_69219,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_4044]) ).
tcf(c_69220,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_dom(sK12))) = apply(sK2,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_68504,c_42224]) ).
tcf(c_69221,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_12701]) ).
tcf(c_69222,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_dom(sK12)))) = sK6(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_10144]) ).
tcf(c_69223,plain,
( ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK12))) = sK15(sK1,sK6(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68504,c_4468]) ).
tcf(c_69259,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(relation_dom(sK1),sK14(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_68508,c_70]) ).
tcf(c_69263,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12))))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_12766]) ).
tcf(c_69264,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12))))) = sK7(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_12765]) ).
tcf(c_69265,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12))))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_10203]) ).
tcf(c_69266,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12))))) = sK7(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_10202]) ).
tcf(c_69267,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_6249]) ).
tcf(c_69268,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_5349]) ).
tcf(c_69270,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_dom(sK12))) = apply(sK1,sK14(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_12284]) ).
tcf(c_69271,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_4619]) ).
tcf(c_69272,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_4406]) ).
tcf(c_69313,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(relation_dom(sK2),sK13(sK1,relation_dom(sK12))) ),
inference(superposition,[status(thm)],[c_68510,c_70]) ).
tcf(c_69317,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_dom(sK12)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_12335]) ).
tcf(c_69318,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12))))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_8396]) ).
tcf(c_69319,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_dom(sK12))))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_8395]) ).
tcf(c_69320,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_4044]) ).
tcf(c_69321,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_dom(sK12))) = apply(sK2,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_68510,c_42224]) ).
tcf(c_69322,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_12701]) ).
tcf(c_69323,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_dom(sK12)))) = sK13(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_10144]) ).
tcf(c_69324,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK12))) = sK15(sK1,sK13(sK1,relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_4468]) ).
tcf(c_69325,plain,
( ( relation_dom(sK2) = relation_dom(sK12) )
| ~ empty(relation_rng(sK12))
| ~ in(sK13(sK1,relation_dom(sK12)),relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_68510,c_10148]) ).
tcf(c_69452,plain,
! [X0: $i] :
( ~ in(X0,relation_rng(sK12))
| ~ in(relation_dom(sK12),sK15(sK12,X0)) ),
inference(superposition,[status(thm)],[c_67988,c_70]) ).
tcf(c_69453,plain,
! [X0: $i] :
( element(sK15(sK12,X0),relation_dom(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_67988,c_69]) ).
tcf(c_69454,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_67988,c_67]) ).
tcf(c_69455,plain,
! [X0: $i] :
( ~ empty(sK12)
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_67988,c_29829]) ).
tcf(c_69456,plain,
! [X0: $i] :
( ~ empty(relation_rng(sK12))
| ~ in(X0,relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_67988,c_68472]) ).
tcf(c_69477,plain,
! [X0: $i] :
( in(sK5(relation_rng(sK12),X0),X0)
| ( relation_dom(relation_rng(sK12)) = X0 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_77,c_69454]) ).
tcf(c_69478,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_dom(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_79,c_69454]) ).
tcf(c_69479,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK12))
| ~ function(relation_rng(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_dom(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_87,c_69454]) ).
tcf(c_69480,plain,
! [X0: $i] :
( in(sK13(relation_rng(sK12),X0),X0)
| ( relation_rng(relation_rng(sK12)) = X0 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_105,c_69454]) ).
tcf(c_69481,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12))
| ~ in(X0,relation_rng(relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_107,c_69454]) ).
tcf(c_69482,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_rng(sK12),X0),sK22(relation_rng(sK12),X0)),X0)
| ( relation_inverse(relation_rng(sK12)) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_69454]) ).
tcf(c_69483,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_rng(sK12)),sK21(X0,relation_rng(sK12))),X0)
| ( relation_inverse(X0) = relation_rng(sK12) )
| ~ relation(X0)
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_125,c_69454]) ).
tcf(c_69484,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_rng(sK12)),sK24(X0,relation_rng(sK12))),X0)
| ( relation_rng(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_69454]) ).
tcf(c_69485,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_rng(sK12),X0),sK24(relation_rng(sK12),X0)),X0)
| ( relation_rng(sK12) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_130,c_69454]) ).
tcf(c_69487,plain,
( element(sK5(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8548,c_69454]) ).
tcf(c_69488,plain,
( element(sK6(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_6286,c_69454]) ).
tcf(c_69489,plain,
( in(sK5(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8302,c_69454]) ).
tcf(c_69490,plain,
( in(sK6(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5335,c_69454]) ).
tcf(c_69491,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5141,c_69454]) ).
tcf(c_69492,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK12),X0) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5420,c_69454]) ).
tcf(c_69493,plain,
( element(sK14(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8430,c_69454]) ).
tcf(c_69494,plain,
( element(sK13(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_6336,c_69454]) ).
tcf(c_69495,plain,
( in(sK14(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8298,c_69454]) ).
tcf(c_69496,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5563,c_69454]) ).
tcf(c_69497,plain,
( in(sK13(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_5542,c_69454]) ).
tcf(c_69498,plain,
( in(sK23(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8327,c_69454]) ).
tcf(c_69499,plain,
( ( relation_rng(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(sK12),sK1)) = sK23(relation_rng(sK12),sK1) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5709,c_69454]) ).
tcf(c_69500,plain,
( in(sK24(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5669,c_69454]) ).
tcf(c_69501,plain,
( in(sK23(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8322,c_69454]) ).
tcf(c_69502,plain,
( ( relation_rng(sK12) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(sK12))) = sK23(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5704,c_69454]) ).
tcf(c_69503,plain,
( in(sK24(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5654,c_69454]) ).
tcf(c_69504,plain,
( in(sK21(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(relation_rng(sK12)) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8332,c_69454]) ).
tcf(c_69505,plain,
( ( relation_inverse(relation_rng(sK12)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_rng(sK12),sK1)) = sK21(relation_rng(sK12),sK1) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5969,c_69454]) ).
tcf(c_69506,plain,
( in(sK22(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK1 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5929,c_69454]) ).
tcf(c_69507,plain,
( in(sK22(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8337,c_69454]) ).
tcf(c_69508,plain,
( ( relation_rng(sK12) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_rng(sK12))) = sK22(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5964,c_69454]) ).
tcf(c_69509,plain,
( in(sK21(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_inverse(sK1) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_5914,c_69454]) ).
tcf(c_69510,plain,
( ( relation_rng(sK12) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8158,c_69454]) ).
tcf(c_69512,plain,
( in(sK23(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23755,c_69454]) ).
tcf(c_69513,plain,
( in(sK24(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18823,c_69454]) ).
tcf(c_69514,plain,
( in(sK5(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_69454]) ).
tcf(c_69515,plain,
( in(sK6(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_69454]) ).
tcf(c_69516,plain,
( in(sK14(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK2) = relation_rng(sK12) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_69454]) ).
tcf(c_69517,plain,
( in(sK13(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK2) = relation_rng(sK12) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_69454]) ).
tcf(c_69518,plain,
( in(sK22(sK2,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23773,c_69454]) ).
tcf(c_69519,plain,
( in(sK21(sK2,relation_rng(sK12)),relation_rng(sK2))
| ( relation_rng(sK12) = relation_inverse(sK2) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18841,c_69454]) ).
tcf(c_69520,plain,
( in(sK21(relation_rng(sK12),sK2),relation_dom(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23767,c_69454]) ).
tcf(c_69521,plain,
( in(sK22(relation_rng(sK12),sK2),relation_rng(sK2))
| ( relation_inverse(relation_rng(sK12)) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18835,c_69454]) ).
tcf(c_69522,plain,
( in(sK23(relation_rng(sK12),sK2),relation_dom(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_23761,c_69454]) ).
tcf(c_69523,plain,
( in(sK24(relation_rng(sK12),sK2),relation_rng(sK2))
| ( relation_rng(sK12) = sK2 )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_18829,c_69454]) ).
tcf(c_69524,plain,
( empty(relation_rng(sK12))
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_36111,c_69454]) ).
tcf(c_69525,plain,
! [X0: $i] :
( ~ empty(relation_dom(sK12))
| ~ in(X0,relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_67825,c_69454]) ).
tcf(c_69984,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12))
| ~ in(relation_dom(sK1),sK5(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_69489,c_70]) ).
tcf(c_69988,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12))))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_12766]) ).
tcf(c_69989,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12))))) = sK7(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_12765]) ).
tcf(c_69990,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12))))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_10203]) ).
tcf(c_69991,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12))))) = sK7(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_10202]) ).
tcf(c_69992,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK15(sK1,apply(sK1,sK5(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_6249]) ).
tcf(c_69993,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12)))) = sK15(sK1,sK7(sK1,sK5(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_5349]) ).
tcf(c_69995,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK5(sK1,relation_rng(sK12))) = apply(sK1,sK5(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_12284]) ).
tcf(c_69996,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_4619]) ).
tcf(c_69997,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_4406]) ).
tcf(c_69998,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12))
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_12287]) ).
tcf(c_70342,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ~ empty(relation_dom(sK12))
| ~ in(relation_dom(sK2),sK6(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_69490,c_70]) ).
tcf(c_70346,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,relation_rng(sK12)))) = apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_12335]) ).
tcf(c_70347,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12))))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_8396]) ).
tcf(c_70348,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,relation_rng(sK12))))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_8395]) ).
tcf(c_70349,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(sK2,sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_4044]) ).
tcf(c_70350,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( sK15(relation_inverse(sK2),sK6(sK1,relation_rng(sK12))) = apply(sK2,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_69490,c_42224]) ).
tcf(c_70351,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_12701]) ).
tcf(c_70352,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,relation_rng(sK12)))) = sK6(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_10144]) ).
tcf(c_70353,plain,
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_rng(sK12))) = sK15(sK1,sK6(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69490,c_4468]) ).
tcf(c_70537,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12))
| ~ in(relation_dom(sK1),sK14(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_69495,c_70]) ).
tcf(c_70541,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12))))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_12766]) ).
tcf(c_70542,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12))))) = sK7(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_12765]) ).
tcf(c_70543,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12))))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_10203]) ).
tcf(c_70544,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12))))) = sK7(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_10202]) ).
tcf(c_70545,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK15(sK1,apply(sK1,sK14(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_6249]) ).
tcf(c_70546,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12)))) = sK15(sK1,sK7(sK1,sK14(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_5349]) ).
tcf(c_70548,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK14(sK1,relation_rng(sK12))) = apply(sK1,sK14(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_12284]) ).
tcf(c_70549,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_4619]) ).
tcf(c_70550,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_4406]) ).
tcf(c_70591,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12))
| ~ in(relation_dom(sK2),sK13(sK1,relation_rng(sK12))) ),
inference(superposition,[status(thm)],[c_69497,c_70]) ).
tcf(c_70595,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,relation_rng(sK12)))) = apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_12335]) ).
tcf(c_70596,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12))))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_8396]) ).
tcf(c_70597,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,relation_rng(sK12))))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_8395]) ).
tcf(c_70598,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(sK2,sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_4044]) ).
tcf(c_70599,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( sK15(relation_inverse(sK2),sK13(sK1,relation_rng(sK12))) = apply(sK2,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_69497,c_42224]) ).
tcf(c_70600,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_12701]) ).
tcf(c_70601,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_10144]) ).
tcf(c_70602,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12))) = sK15(sK1,sK13(sK1,relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_4468]) ).
tcf(c_70603,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ~ empty(relation_dom(sK12))
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_69497,c_10148]) ).
tcf(c_70648,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_9713,c_14030]) ).
tcf(c_70649,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_4763,c_14030]) ).
tcf(c_70653,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_87]) ).
tcf(c_70654,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_12599]) ).
tcf(c_70655,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_61586]) ).
tcf(c_70657,plain,
( in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14030,c_57811]) ).
tcf(c_70663,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK2),sK5(empty_set,relation_dom(sK2)))
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_6246]) ).
tcf(c_70664,plain,
( element(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_6247]) ).
tcf(c_70665,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_5332]) ).
tcf(c_70688,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70653,c_65,c_64]) ).
tcf(c_70737,plain,
( in(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_70688]) ).
tcf(c_70738,plain,
( in(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_70688]) ).
tcf(c_70739,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_70688,c_70]) ).
tcf(c_70740,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70688,c_69]) ).
tcf(c_70742,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70688,c_106]) ).
tcf(c_70748,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_70742,c_4013]) ).
tcf(c_70788,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34013,c_14032]) ).
tcf(c_70792,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_87]) ).
tcf(c_70793,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_12599]) ).
tcf(c_70794,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_61586]) ).
tcf(c_70795,plain,
( in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14032,c_57811]) ).
tcf(c_70796,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = sK15(sK1,sK5(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14032,c_57193]) ).
tcf(c_70801,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(relation_dom(sK2),sK5(empty_set,relation_dom(sK2)))
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_6246]) ).
tcf(c_70802,plain,
( element(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_6247]) ).
tcf(c_70803,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_5332]) ).
tcf(c_70804,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14032,c_4791]) ).
tcf(c_70805,plain,
( ( relation_dom(sK2) = empty_set )
| ( sK5(empty_set,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_14032,c_10494]) ).
tcf(c_70831,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70792,c_65,c_64]) ).
tcf(c_70877,plain,
! [X0: $i] :
( ( apply(X0,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_dom(X0)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_9702]) ).
tcf(c_70878,plain,
( ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_dom(sK1)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_9702]) ).
tcf(c_70879,plain,
( ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_9702]) ).
tcf(c_70881,plain,
apply(relation_inverse(sK1),relation_dom(sK2)) = empty_set,
inference(superposition,[status(thm)],[c_4546,c_9702]) ).
tcf(c_70883,plain,
( ( apply(relation_inverse(sK12),relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_rng(sK12)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_9702]) ).
tcf(c_70909,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_70881,c_87]) ).
tcf(c_70910,plain,
( in(relation_dom(sK2),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70881,c_13473]) ).
tcf(c_70911,plain,
( element(relation_dom(sK2),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70881,c_13472]) ).
tcf(c_70918,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(relation_inverse(sK1),relation_dom(sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70881,c_13488]) ).
tcf(c_70919,plain,
( ( apply(sK1,empty_set) = relation_dom(sK2) )
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_70881,c_12807]) ).
tcf(c_70920,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70881,c_4623]) ).
tcf(c_70921,plain,
( ( sK15(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_70881,c_4763]) ).
tcf(c_70936,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_70918,c_70881]) ).
tcf(c_70940,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_70909,c_4030]) ).
tcf(c_70941,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_70940,c_987,c_3611]) ).
tcf(c_70961,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_70831]) ).
tcf(c_70962,plain,
( ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_70831,c_70]) ).
tcf(c_70963,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70831,c_69]) ).
tcf(c_70965,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70831,c_106]) ).
tcf(c_70970,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70831,c_3784]) ).
tcf(c_70971,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_70965,c_4013]) ).
tcf(c_70990,plain,
( ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ in(relation_inverse(sK1),ordered_pair(relation_dom(sK2),empty_set)) ),
inference(superposition,[status(thm)],[c_70941,c_70]) ).
tcf(c_70991,plain,
( element(ordered_pair(relation_dom(sK2),empty_set),relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70941,c_69]) ).
tcf(c_70993,plain,
( in(empty_set,relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70941,c_106]) ).
tcf(c_70994,plain,
( in(relation_dom(sK2),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70941,c_78]) ).
tcf(c_70996,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ~ relation(sK1)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70941,c_297]) ).
tcf(c_71003,plain,
( in(empty_set,relation_dom(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_70993,c_3821]) ).
tcf(c_71004,plain,
( in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71003,c_3611]) ).
tcf(c_71012,plain,
( in(empty_set,relation_dom(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_71004]) ).
tcf(c_71015,plain,
( in(empty_set,relation_dom(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71012,c_62,c_61]) ).
tcf(c_71022,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK1),empty_set) ),
inference(superposition,[status(thm)],[c_71015,c_70]) ).
tcf(c_71023,plain,
( element(empty_set,relation_dom(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71015,c_69]) ).
tcf(c_71026,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,empty_set))) = apply(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_71015,c_12766]) ).
tcf(c_71027,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,empty_set))) = sK7(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_71015,c_12765]) ).
tcf(c_71028,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,empty_set))) = apply(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_71015,c_10203]) ).
tcf(c_71029,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,empty_set))) = sK7(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_71015,c_10202]) ).
tcf(c_71030,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,empty_set)) = sK15(sK1,apply(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_71015,c_6249]) ).
tcf(c_71031,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,empty_set)) = sK15(sK1,sK7(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_71015,c_5349]) ).
tcf(c_71033,plain,
( ( sK15(relation_inverse(sK1),empty_set) = apply(sK1,empty_set) )
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71015,c_12284]) ).
tcf(c_71034,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71015,c_4619]) ).
tcf(c_71035,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71015,c_4406]) ).
tcf(c_71073,plain,
( ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70919,c_19430]) ).
tcf(c_71074,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70919,c_4045]) ).
tcf(c_71075,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70919,c_19431]) ).
tcf(c_71076,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70919,c_18734]) ).
tcf(c_71077,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70919,c_87]) ).
tcf(c_71093,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71077,c_62,c_61]) ).
tcf(c_71114,plain,
( ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ in(sK2,ordered_pair(relation_dom(sK2),empty_set)) ),
inference(superposition,[status(thm)],[c_71093,c_70]) ).
tcf(c_71115,plain,
( element(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71093,c_69]) ).
tcf(c_71117,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ relation(sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71093,c_106]) ).
tcf(c_71125,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71117,c_61]) ).
tcf(c_71148,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),sK15(sK1,sK5(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_14034,c_87]) ).
tcf(c_71149,plain,
( in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14034,c_13473]) ).
tcf(c_71150,plain,
( element(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14034,c_13472]) ).
tcf(c_71151,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_14034,c_34564]) ).
tcf(c_71152,plain,
( element(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14034,c_34565]) ).
tcf(c_71153,plain,
( in(sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14034,c_34571]) ).
tcf(c_71154,plain,
( in(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14034,c_34529]) ).
tcf(c_71158,plain,
( in(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14034,c_4623]) ).
tcf(c_71159,plain,
( in(ordered_pair(sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14034,c_70688]) ).
tcf(c_71160,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK15(sK1,sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_14034,c_14030]) ).
tcf(c_71192,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),sK15(sK1,sK5(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_71148,c_4030]) ).
tcf(c_71193,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),sK15(sK1,sK5(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71192,c_987,c_3611]) ).
tcf(c_71266,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ relation(sK1)
| ~ in(relation_dom(sK2),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_70921,c_107]) ).
tcf(c_71267,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70921,c_12678]) ).
tcf(c_71273,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK15(sK1,relation_dom(sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_70921,c_14876]) ).
tcf(c_71275,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK1),empty_set)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70921,c_8391]) ).
tcf(c_71284,plain,
( in(ordered_pair(empty_set,relation_dom(sK2)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ relation(sK1)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_71266,c_4013]) ).
tcf(c_71290,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(empty_set,relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_71033,c_107]) ).
tcf(c_71291,plain,
( in(ordered_pair(empty_set,apply(sK1,empty_set)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71033,c_4472]) ).
tcf(c_71295,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(empty_set,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_71290,c_3821]) ).
tcf(c_71296,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71295,c_3611]) ).
tcf(c_71310,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_71034,c_87]) ).
tcf(c_71311,plain,
( in(apply(sK1,empty_set),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71034,c_13473]) ).
tcf(c_71312,plain,
( element(apply(sK1,empty_set),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71034,c_13472]) ).
tcf(c_71317,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,apply(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71034,c_9713]) ).
tcf(c_71318,plain,
( in(ordered_pair(empty_set,apply(sK1,empty_set)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71034,c_13488]) ).
tcf(c_71319,plain,
( in(ordered_pair(empty_set,apply(sK1,empty_set)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71034,c_4623]) ).
tcf(c_71320,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,apply(sK1,empty_set)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71034,c_4763]) ).
tcf(c_71321,plain,
( ( apply(sK1,empty_set) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,apply(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71034,c_56725]) ).
tcf(c_71345,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_71310,c_4030]) ).
tcf(c_71346,plain,
( in(ordered_pair(apply(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71345,c_987,c_3611]) ).
tcf(c_71584,plain,
( in(ordered_pair(sK7(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_71035,c_87]) ).
tcf(c_71585,plain,
( in(ordered_pair(empty_set,sK7(sK1,empty_set)),sK1)
| ( apply(sK1,empty_set) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71035,c_64231]) ).
tcf(c_71586,plain,
( ( apply(sK1,empty_set) = empty_set )
| ( apply(sK1,empty_set) = sK7(sK1,empty_set) )
| ( apply(sK2,relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71035,c_63810]) ).
tcf(c_71587,plain,
( ( apply(sK1,empty_set) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,sK7(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71035,c_55855]) ).
tcf(c_71588,plain,
( in(sK7(sK1,empty_set),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71035,c_13473]) ).
tcf(c_71589,plain,
( element(sK7(sK1,empty_set),relation_dom(sK2))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71035,c_13472]) ).
tcf(c_71595,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,sK7(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71035,c_9713]) ).
tcf(c_71596,plain,
( in(ordered_pair(empty_set,sK7(sK1,empty_set)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71035,c_13488]) ).
tcf(c_71597,plain,
( ( apply(sK1,empty_set) = sK7(sK1,empty_set) )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71035,c_12807]) ).
tcf(c_71598,plain,
( in(ordered_pair(empty_set,sK7(sK1,empty_set)),sK1)
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK7(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_71035,c_4623]) ).
tcf(c_71599,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,sK7(sK1,empty_set)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71035,c_4763]) ).
tcf(c_71633,plain,
( in(ordered_pair(sK7(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_71584,c_4030]) ).
tcf(c_71634,plain,
( in(ordered_pair(sK7(sK1,empty_set),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK7(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71633,c_987,c_3611]) ).
tcf(c_71709,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_12147]) ).
tcf(c_71710,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_12147]) ).
tcf(c_71711,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_12147]) ).
tcf(c_71712,plain,
! [X0: $i] :
( ( sK20(powerset(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_12147]) ).
tcf(c_71713,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_12147]) ).
tcf(c_71714,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_12147]) ).
tcf(c_71737,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_28999]) ).
tcf(c_71738,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_28999]) ).
tcf(c_71739,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_28999]) ).
tcf(c_71740,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_28999]) ).
tcf(c_71741,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_28999]) ).
tcf(c_71742,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_28999]) ).
tcf(c_71778,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_64169,c_64168]) ).
tcf(c_71782,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_87]) ).
tcf(c_71783,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_12599]) ).
tcf(c_71784,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_61586]) ).
tcf(c_71785,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_64168,c_61136]) ).
tcf(c_71786,plain,
! [X0: $i] :
( in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64168,c_57811]) ).
tcf(c_71791,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK2),sK7(sK1,X0))
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_6246]) ).
tcf(c_71792,plain,
! [X0: $i] :
( element(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_6247]) ).
tcf(c_71793,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_5332]) ).
tcf(c_71817,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_71782,c_65,c_64]) ).
tcf(c_72026,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56204,c_71817]) ).
tcf(c_72027,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64169,c_71817]) ).
tcf(c_72029,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_71817,c_70]) ).
tcf(c_72030,plain,
! [X0: $i] :
( element(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71817,c_69]) ).
tcf(c_72032,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_71817,c_106]) ).
tcf(c_72041,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_72032,c_4013]) ).
tcf(c_72064,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_14967,c_107]) ).
tcf(c_72065,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14967,c_12678]) ).
tcf(c_72067,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_14967,c_59117]) ).
tcf(c_72068,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_14967,c_58270]) ).
tcf(c_72070,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14967,c_34537]) ).
tcf(c_72071,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14967,c_14876]) ).
tcf(c_72072,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(relation_dom(sK1),sK13(sK1,relation_dom(sK1)))
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14967,c_8391]) ).
tcf(c_72073,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14967,c_8392]) ).
tcf(c_72074,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14967,c_8294]) ).
tcf(c_72113,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_72064,c_4013]) ).
tcf(c_72121,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29000]) ).
tcf(c_72122,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29000]) ).
tcf(c_72123,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29000]) ).
tcf(c_72124,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29000]) ).
tcf(c_72125,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29000]) ).
tcf(c_72126,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29000]) ).
tcf(c_72149,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29001]) ).
tcf(c_72150,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29001]) ).
tcf(c_72151,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29001]) ).
tcf(c_72152,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29001]) ).
tcf(c_72153,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29001]) ).
tcf(c_72154,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29001]) ).
tcf(c_72177,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29046]) ).
tcf(c_72178,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29046]) ).
tcf(c_72179,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29046]) ).
tcf(c_72180,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29046]) ).
tcf(c_72181,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29046]) ).
tcf(c_72182,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29046]) ).
tcf(c_72205,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29047]) ).
tcf(c_72206,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29047]) ).
tcf(c_72207,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29047]) ).
tcf(c_72208,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29047]) ).
tcf(c_72209,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29047]) ).
tcf(c_72210,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29047]) ).
tcf(c_72236,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK2),X0) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),X0) ),
inference(superposition,[status(thm)],[c_4510,c_70]) ).
tcf(c_72237,plain,
! [X0: $i] :
( element(X0,relation_rng(sK2))
| ( apply(relation_inverse(sK2),X0) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_69]) ).
tcf(c_72239,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK2)) = X0 )
| ( apply(relation_inverse(sK2),ordered_pair(sK5(relation_rng(sK2),X0),X1)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(sK5(relation_rng(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_4510,c_76]) ).
tcf(c_72240,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_rng(sK2)))
| ( apply(relation_inverse(sK2),ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_106]) ).
tcf(c_72241,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_rng(sK2)))
| ( apply(relation_inverse(sK2),ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_78]) ).
tcf(c_72242,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_rng(sK2),X0) = X1 )
| ( apply(relation_inverse(sK2),ordered_pair(X0,X1)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ function(relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_197]) ).
tcf(c_72243,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK2)) = X0 )
| ( apply(relation_inverse(sK2),ordered_pair(X1,sK13(relation_rng(sK2),X0))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(sK13(relation_rng(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_4510,c_104]) ).
tcf(c_72244,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK2)) = X0 )
| ( apply(relation_inverse(sK2),ordered_pair(sK22(relation_rng(sK2),X0),sK21(relation_rng(sK2),X0))) = empty_set )
| ~ relation(X0)
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0) ),
inference(superposition,[status(thm)],[c_4510,c_124]) ).
tcf(c_72245,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK2),ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2)))) = empty_set )
| ~ relation(X0)
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_rng(sK2))
| ~ in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0) ),
inference(superposition,[status(thm)],[c_4510,c_129]) ).
tcf(c_72246,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK2),X0) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),X0)) = X0 )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_43161]) ).
tcf(c_72247,plain,
( ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK2))) = empty_set )
| ( apply(relation_inverse(sK2),sK5(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_12622]) ).
tcf(c_72248,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(relation_inverse(sK2),sK13(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_10578]) ).
tcf(c_72249,plain,
( ( apply(relation_inverse(sK2),relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_rng(sK2)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_9702]) ).
tcf(c_72250,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_rng(sK2))) = empty_set )
| ( apply(relation_inverse(sK2),sK5(sK2,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_43088]) ).
tcf(c_72252,plain,
! [X0: $i] :
( ( relation_rng(sK2) = X0 )
| ( apply(relation_inverse(sK2),sK13(sK2,X0)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_4510,c_43165]) ).
tcf(c_72355,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK7(sK1,sK13(sK1,relation_dom(sK1))) = apply(sK1,empty_set) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15829,c_52427]) ).
tcf(c_72356,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15829,c_19430]) ).
tcf(c_72357,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15829,c_4045]) ).
tcf(c_72358,plain,
( element(empty_set,relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15829,c_19431]) ).
tcf(c_72359,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15829,c_18734]) ).
tcf(c_72360,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),empty_set),sK2)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15829,c_87]) ).
tcf(c_72384,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),empty_set),sK2)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72360,c_62,c_61]) ).
tcf(c_72417,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29048]) ).
tcf(c_72418,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29048]) ).
tcf(c_72419,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29048]) ).
tcf(c_72420,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29048]) ).
tcf(c_72421,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29048]) ).
tcf(c_72422,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29048]) ).
tcf(c_72445,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29432]) ).
tcf(c_72446,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29432]) ).
tcf(c_72447,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29432]) ).
tcf(c_72448,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29432]) ).
tcf(c_72449,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29432]) ).
tcf(c_72450,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29432]) ).
tcf(c_72473,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29433]) ).
tcf(c_72474,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29433]) ).
tcf(c_72475,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29433]) ).
tcf(c_72476,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29433]) ).
tcf(c_72477,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29433]) ).
tcf(c_72478,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29433]) ).
tcf(c_72501,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_dom(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_29434]) ).
tcf(c_72502,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_rng(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_29434]) ).
tcf(c_72503,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(X0))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_29434]) ).
tcf(c_72504,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(empty_set)) = X0 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_136,c_29434]) ).
tcf(c_72505,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_29434]) ).
tcf(c_72506,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_29434]) ).
tcf(c_72534,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ in(sK2,ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),empty_set)) ),
inference(superposition,[status(thm)],[c_72384,c_70]) ).
tcf(c_72535,plain,
( element(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),empty_set),sK2)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_72384,c_69]) ).
tcf(c_72537,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ relation(sK2)
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_72384,c_106]) ).
tcf(c_72542,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72537,c_61]) ).
tcf(c_72571,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_72542]) ).
tcf(c_72611,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56204,c_4848]) ).
tcf(c_72612,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_57193,c_4848]) ).
tcf(c_72613,plain,
( in(ordered_pair(apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14967,c_4848]) ).
tcf(c_72614,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70921,c_4848]) ).
tcf(c_72615,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2))
| ~ in(relation_inverse(sK1),ordered_pair(X0,sK15(sK1,X0))) ),
inference(superposition,[status(thm)],[c_4848,c_70]) ).
tcf(c_72616,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4848,c_69]) ).
tcf(c_72618,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK1)) = X0 )
| ( apply(sK2,sK5(relation_inverse(sK1),X0)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(relation_inverse(sK1),X0),X0)
| ~ in(sK5(relation_inverse(sK1),X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4848,c_76]) ).
tcf(c_72619,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4848,c_106]) ).
tcf(c_72620,plain,
! [X0: $i] :
( in(X0,relation_dom(relation_inverse(sK1)))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4848,c_78]) ).
tcf(c_72622,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ~ relation(sK1)
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4848,c_297]) ).
tcf(c_72635,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_72619,c_3821]) ).
tcf(c_72645,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(relation_inverse(sK1),X0)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(relation_inverse(sK1),X0),X0)
| ~ in(sK5(relation_inverse(sK1),X0),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_72618,c_4030]) ).
tcf(c_72646,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK5(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK5(relation_inverse(sK1),X0),X0)
| ~ in(sK5(relation_inverse(sK1),X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72645,c_3611]) ).
tcf(c_72667,plain,
! [X0: $i] :
( ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_inverse(X0))) = sK5(sK1,relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_5248]) ).
tcf(c_72682,plain,
! [X0: $i] :
( ( relation_inverse(X0) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_inverse(X0))) = sK14(sK1,relation_inverse(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_6419]) ).
tcf(c_72698,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_6474]) ).
tcf(c_72700,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_6474]) ).
tcf(c_72701,plain,
( in(sK24(sK1,relation_inverse(sK2)),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_6474]) ).
tcf(c_72702,plain,
( in(sK24(sK1,relation_inverse(sK9)),relation_dom(sK9))
| in(sK24(sK1,relation_inverse(sK9)),relation_dom(sK2))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_6474]) ).
tcf(c_72703,plain,
( in(sK24(sK1,relation_inverse(sK10)),relation_dom(sK10))
| in(sK24(sK1,relation_inverse(sK10)),relation_dom(sK2))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_6474]) ).
tcf(c_72705,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK24(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6474,c_70]) ).
tcf(c_72706,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| element(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6474,c_69]) ).
tcf(c_72707,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6474,c_67]) ).
tcf(c_72708,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6474,c_43161]) ).
tcf(c_72709,plain,
( in(sK24(sK1,sK9),relation_dom(sK2))
| ( sK1 = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6474,c_29938]) ).
tcf(c_72710,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_6474,c_69454]) ).
tcf(c_72715,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72710,c_95]) ).
tcf(c_72719,plain,
( in(sK24(sK1,sK9),relation_dom(sK2))
| ( sK1 = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72709,c_83]) ).
tcf(c_72743,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72700,c_3610]) ).
tcf(c_72747,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_72698,c_3611]) ).
tcf(c_72939,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(sK1,relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_72701,c_70]) ).
tcf(c_72940,plain,
( element(sK24(sK1,relation_inverse(sK2)),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_69]) ).
tcf(c_72943,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,relation_inverse(sK2)))) = apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_12335]) ).
tcf(c_72944,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK2))))) = sK15(sK1,sK24(sK1,relation_inverse(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_8396]) ).
tcf(c_72945,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK2))))) = sK15(sK1,sK24(sK1,relation_inverse(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_8395]) ).
tcf(c_72946,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,relation_inverse(sK2)))) = sK24(sK1,relation_inverse(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_4044]) ).
tcf(c_72947,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,relation_inverse(sK2))) = apply(sK2,sK24(sK1,relation_inverse(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_42224]) ).
tcf(c_72948,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK2)))) = sK24(sK1,relation_inverse(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_12701]) ).
tcf(c_72949,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,relation_inverse(sK2)))) = sK24(sK1,relation_inverse(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_10144]) ).
tcf(c_72950,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK2))) = sK15(sK1,sK24(sK1,relation_inverse(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72701,c_4468]) ).
tcf(c_73216,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_15831,c_107]) ).
tcf(c_73217,plain,
( in(ordered_pair(sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15831,c_4848]) ).
tcf(c_73219,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15831,c_12678]) ).
tcf(c_73221,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_15831,c_59117]) ).
tcf(c_73222,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_15831,c_58270]) ).
tcf(c_73224,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_15831,c_34537]) ).
tcf(c_73225,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15831,c_14876]) ).
tcf(c_73227,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(relation_dom(sK1),sK13(sK1,relation_dom(sK1)))
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15831,c_8391]) ).
tcf(c_73228,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15831,c_8392]) ).
tcf(c_73229,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_15831,c_8294]) ).
tcf(c_73230,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15831,c_71817]) ).
tcf(c_73280,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_73216,c_4013]) ).
tcf(c_73293,plain,
! [X0: $i] :
( ( apply(X0,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(X0)) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_31455]) ).
tcf(c_73294,plain,
( ( apply(sK1,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK1)) = empty_set )
| ( apply(sK2,apply(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_31455]) ).
tcf(c_73295,plain,
( ( apply(sK1,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_31455]) ).
tcf(c_73296,plain,
( ( apply(sK2,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_31455]) ).
tcf(c_73298,plain,
( ( apply(relation_inverse(sK12),relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_rng(sK12)) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_31455]) ).
tcf(c_73300,plain,
apply(relation_inverse(sK12),relation_rng(sK12)) = empty_set,
inference(superposition,[status(thm)],[c_5420,c_31455]) ).
tcf(c_73324,plain,
! [X0: $i] :
( in(sK20(sK20(powerset(X0))),X0)
| empty(sK20(powerset(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_34292,c_11848,c_34292]) ).
tcf(c_73325,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| in(sK20(sK20(powerset(X0))),X0) ),
inference(renaming,[status(thm)],[c_73324]) ).
tcf(c_73331,plain,
( empty(sK20(powerset(empty_set)))
| in(sK20(empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_14781,c_73325]) ).
tcf(c_73332,plain,
! [X0: $i] :
( empty(sK20(powerset(relation_rng(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73325,c_30414]) ).
tcf(c_73333,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| ~ in(X0,sK20(sK20(powerset(X0)))) ),
inference(superposition,[status(thm)],[c_73325,c_70]) ).
tcf(c_73336,plain,
! [X0: $i] :
( empty(sK20(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73325,c_29829]) ).
tcf(c_73337,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK20(sK20(powerset(relation_dom(sK1))))))) = apply(sK1,sK20(sK20(powerset(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_12766]) ).
tcf(c_73338,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK20(sK20(powerset(relation_dom(sK1))))))) = sK7(sK1,sK20(sK20(powerset(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_12765]) ).
tcf(c_73339,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(sK20(powerset(relation_dom(sK1))))))) = apply(sK1,sK20(sK20(powerset(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_10203]) ).
tcf(c_73340,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(sK20(powerset(relation_dom(sK1))))))) = sK7(sK1,sK20(sK20(powerset(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_10202]) ).
tcf(c_73341,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) = sK15(sK1,apply(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_6249]) ).
tcf(c_73342,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) = sK15(sK1,sK7(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_5349]) ).
tcf(c_73344,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( sK15(relation_inverse(sK1),sK20(sK20(powerset(relation_dom(sK1))))) = apply(sK1,sK20(sK20(powerset(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_12284]) ).
tcf(c_73345,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) = sK20(sK20(powerset(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_4619]) ).
tcf(c_73346,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) = sK20(sK20(powerset(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_4406]) ).
tcf(c_73347,plain,
empty(sK20(powerset(empty_set))),
inference(superposition,[status(thm)],[c_73325,c_8115]) ).
tcf(c_73348,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(sK20(powerset(relation_dom(sK2)))))) = apply(sK1,sK15(sK1,sK20(sK20(powerset(relation_dom(sK2)))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_12335]) ).
tcf(c_73349,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(sK20(powerset(relation_dom(sK2))))))) = sK15(sK1,sK20(sK20(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_8396]) ).
tcf(c_73350,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(sK20(powerset(relation_dom(sK2))))))) = sK15(sK1,sK20(sK20(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_8395]) ).
tcf(c_73351,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(sK20(powerset(relation_dom(sK2)))))) = sK20(sK20(powerset(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_4044]) ).
tcf(c_73352,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( sK15(relation_inverse(sK2),sK20(sK20(powerset(relation_dom(sK2))))) = apply(sK2,sK20(sK20(powerset(relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_73325,c_42224]) ).
tcf(c_73353,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( apply(sK1,apply(relation_inverse(sK1),sK20(sK20(powerset(relation_dom(sK2)))))) = sK20(sK20(powerset(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_12701]) ).
tcf(c_73354,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(sK20(powerset(relation_dom(sK2)))))) = sK20(sK20(powerset(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_10144]) ).
tcf(c_73355,plain,
( empty(sK20(powerset(relation_dom(sK2))))
| ( apply(relation_inverse(sK1),sK20(sK20(powerset(relation_dom(sK2))))) = sK15(sK1,sK20(sK20(powerset(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_73325,c_4468]) ).
tcf(c_73356,plain,
! [X0: $i] :
( empty(X0)
| empty(sK20(powerset(sK19(X0))))
| element(sK20(sK20(powerset(sK19(X0)))),X0) ),
inference(superposition,[status(thm)],[c_73325,c_4215]) ).
tcf(c_73357,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(powerset(X0)))))
| element(sK20(sK20(powerset(sK20(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_73325,c_4216]) ).
tcf(c_73358,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73325,c_4201]) ).
tcf(c_73359,plain,
( empty(sK20(powerset(relation_rng(sK2))))
| ( apply(sK2,sK7(relation_inverse(sK2),sK20(sK20(powerset(relation_rng(sK2)))))) = sK20(sK20(powerset(relation_rng(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_73325,c_43161]) ).
tcf(c_73360,plain,
( empty(sK20(powerset(relation_rng(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73325,c_29938]) ).
tcf(c_73361,plain,
( empty(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73325,c_69454]) ).
tcf(c_73362,plain,
( empty(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73325,c_29940]) ).
tcf(c_73363,plain,
( empty(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73325,c_68472]) ).
tcf(c_73364,plain,
( empty(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73325,c_30499]) ).
tcf(c_73365,plain,
( empty(sK20(powerset(relation_dom(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73325,c_30501]) ).
tcf(c_73366,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(sK19(powerset(X0))))))
| element(sK20(sK20(powerset(sK20(sK19(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_73325,c_36119]) ).
tcf(c_73367,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(sK19(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73325,c_36116]) ).
tcf(c_73373,plain,
( empty(empty_set)
| in(sK20(empty_set),empty_set) ),
inference(light_normalisation,[status(thm)],[c_73331,c_14781]) ).
tcf(c_73449,plain,
( empty(sK20(powerset(empty_set)))
| ~ in(empty_set,sK20(empty_set)) ),
inference(superposition,[status(thm)],[c_14781,c_73333]) ).
tcf(c_73450,plain,
( empty(empty_set)
| ~ in(empty_set,sK20(empty_set)) ),
inference(light_normalisation,[status(thm)],[c_73449,c_14781]) ).
tcf(c_73454,plain,
( in(ordered_pair(relation_rng(sK12),empty_set),relation_inverse(sK12))
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(relation_rng(sK12),relation_dom(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_73300,c_87]) ).
tcf(c_73457,plain,
( in(ordered_pair(relation_rng(sK12),empty_set),relation_inverse(sK12))
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(relation_rng(sK12),relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_73454,c_3810]) ).
tcf(c_73458,plain,
( in(ordered_pair(relation_rng(sK12),empty_set),relation_inverse(sK12))
| ~ in(relation_rng(sK12),relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_73457,c_1001,c_3610]) ).
tcf(c_73478,plain,
( empty(sK20(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3424,c_73332]) ).
tcf(c_73483,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(X0))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_rng(X0))))) = sK14(sK1,sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_6419]) ).
tcf(c_73484,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(X0))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_rng(X0))))) = sK5(sK1,sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_5248]) ).
tcf(c_73485,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29434]) ).
tcf(c_73486,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29433]) ).
tcf(c_73487,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29432]) ).
tcf(c_73488,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29048]) ).
tcf(c_73489,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29047]) ).
tcf(c_73490,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29046]) ).
tcf(c_73491,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29001]) ).
tcf(c_73492,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_29000]) ).
tcf(c_73493,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_28999]) ).
tcf(c_73494,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(relation_rng(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12147]) ).
tcf(c_73495,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3853]) ).
tcf(c_73496,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3852]) ).
tcf(c_73497,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3847]) ).
tcf(c_73498,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3813]) ).
tcf(c_73499,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3812]) ).
tcf(c_73500,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3807]) ).
tcf(c_73501,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_39387]) ).
tcf(c_73502,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_39386]) ).
tcf(c_73503,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_39385]) ).
tcf(c_73504,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34275]) ).
tcf(c_73505,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34274]) ).
tcf(c_73506,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34273]) ).
tcf(c_73507,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34257]) ).
tcf(c_73508,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34256]) ).
tcf(c_73509,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_34255]) ).
tcf(c_73510,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_27401]) ).
tcf(c_73511,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_27400]) ).
tcf(c_73512,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_27399]) ).
tcf(c_73513,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25347]) ).
tcf(c_73514,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25346]) ).
tcf(c_73515,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25345]) ).
tcf(c_73516,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25312]) ).
tcf(c_73517,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25311]) ).
tcf(c_73518,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25310]) ).
tcf(c_73519,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25248]) ).
tcf(c_73520,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25247]) ).
tcf(c_73521,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25246]) ).
tcf(c_73522,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24512]) ).
tcf(c_73523,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24511]) ).
tcf(c_73524,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24510]) ).
tcf(c_73525,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24398]) ).
tcf(c_73526,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24397]) ).
tcf(c_73527,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24396]) ).
tcf(c_73528,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24361]) ).
tcf(c_73529,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24360]) ).
tcf(c_73530,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24359]) ).
tcf(c_73531,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24299]) ).
tcf(c_73532,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24298]) ).
tcf(c_73533,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24297]) ).
tcf(c_73534,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23557]) ).
tcf(c_73535,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23556]) ).
tcf(c_73536,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23555]) ).
tcf(c_73537,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23520]) ).
tcf(c_73538,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23519]) ).
tcf(c_73539,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23518]) ).
tcf(c_73540,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23406]) ).
tcf(c_73541,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23405]) ).
tcf(c_73542,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23404]) ).
tcf(c_73543,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23371]) ).
tcf(c_73544,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23370]) ).
tcf(c_73545,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23369]) ).
tcf(c_73546,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_22305]) ).
tcf(c_73547,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_22304]) ).
tcf(c_73548,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_22303]) ).
tcf(c_73549,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_21079]) ).
tcf(c_73550,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_21078]) ).
tcf(c_73551,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_21077]) ).
tcf(c_73552,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20790]) ).
tcf(c_73553,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20789]) ).
tcf(c_73554,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20788]) ).
tcf(c_73555,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20733]) ).
tcf(c_73556,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20732]) ).
tcf(c_73557,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20731]) ).
tcf(c_73558,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14787]) ).
tcf(c_73559,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20567]) ).
tcf(c_73560,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20566]) ).
tcf(c_73561,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20565]) ).
tcf(c_73562,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19623]) ).
tcf(c_73563,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14242]) ).
tcf(c_73564,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14162]) ).
tcf(c_73565,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14077]) ).
tcf(c_73566,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12144]) ).
tcf(c_73567,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19622]) ).
tcf(c_73568,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19621]) ).
tcf(c_73569,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12143]) ).
tcf(c_73570,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12142]) ).
tcf(c_73571,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12141]) ).
tcf(c_73572,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12140]) ).
tcf(c_73573,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19044]) ).
tcf(c_73574,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19043]) ).
tcf(c_73575,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12139]) ).
tcf(c_73576,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19042]) ).
tcf(c_73577,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18986]) ).
tcf(c_73578,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18985]) ).
tcf(c_73579,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18984]) ).
tcf(c_73580,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_36589]) ).
tcf(c_73581,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18933]) ).
tcf(c_73582,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18932]) ).
tcf(c_73583,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18931]) ).
tcf(c_73584,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18887]) ).
tcf(c_73585,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18886]) ).
tcf(c_73586,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18885]) ).
tcf(c_73587,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18057]) ).
tcf(c_73588,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18056]) ).
tcf(c_73589,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18055]) ).
tcf(c_73590,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17694]) ).
tcf(c_73591,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17693]) ).
tcf(c_73592,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17692]) ).
tcf(c_73593,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17624]) ).
tcf(c_73594,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17623]) ).
tcf(c_73595,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17622]) ).
tcf(c_73596,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17580]) ).
tcf(c_73597,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17579]) ).
tcf(c_73598,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17578]) ).
tcf(c_73599,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17545]) ).
tcf(c_73600,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17544]) ).
tcf(c_73601,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17543]) ).
tcf(c_73602,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_16055]) ).
tcf(c_73603,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_16054]) ).
tcf(c_73604,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_16053]) ).
tcf(c_73605,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15952]) ).
tcf(c_73606,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15951]) ).
tcf(c_73607,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15950]) ).
tcf(c_73608,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15917]) ).
tcf(c_73609,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15916]) ).
tcf(c_73610,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15915]) ).
tcf(c_73611,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15880]) ).
tcf(c_73612,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15879]) ).
tcf(c_73613,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15878]) ).
tcf(c_73614,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12149]) ).
tcf(c_73615,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12148]) ).
tcf(c_73616,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))) = relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11026]) ).
tcf(c_73617,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(relation_rng(X0))))) = relation_inverse(relation_rng(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11025]) ).
tcf(c_73618,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(relation_rng(X0))))) = relation_inverse(relation_dom(sK20(powerset(relation_rng(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11024]) ).
tcf(c_73619,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3663]) ).
tcf(c_73620,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(relation_rng(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3662]) ).
tcf(c_73621,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(relation_rng(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3661]) ).
tcf(c_73622,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = relation_rng(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3632]) ).
tcf(c_73623,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_12146]) ).
tcf(c_73624,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = relation_inverse(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3631]) ).
tcf(c_73625,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = relation_dom(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_3626]) ).
tcf(c_73626,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14780]) ).
tcf(c_73627,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14779]) ).
tcf(c_73628,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14778]) ).
tcf(c_73629,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14235]) ).
tcf(c_73630,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14234]) ).
tcf(c_73631,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14233]) ).
tcf(c_73632,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14155]) ).
tcf(c_73633,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14154]) ).
tcf(c_73634,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14153]) ).
tcf(c_73635,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14070]) ).
tcf(c_73636,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14069]) ).
tcf(c_73637,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_14068]) ).
tcf(c_73638,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11811]) ).
tcf(c_73639,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11810]) ).
tcf(c_73640,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11809]) ).
tcf(c_73641,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11771]) ).
tcf(c_73642,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11770]) ).
tcf(c_73643,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11769]) ).
tcf(c_73644,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11729]) ).
tcf(c_73645,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11728]) ).
tcf(c_73646,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11727]) ).
tcf(c_73647,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11691]) ).
tcf(c_73648,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11690]) ).
tcf(c_73649,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11689]) ).
tcf(c_73650,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11660]) ).
tcf(c_73651,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11659]) ).
tcf(c_73652,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11658]) ).
tcf(c_73653,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11297]) ).
tcf(c_73654,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11296]) ).
tcf(c_73655,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_11295]) ).
tcf(c_73666,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(relation_rng(X0)))) = relation_inverse(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_957]) ).
tcf(c_73672,plain,
! [X0: $i] :
( relation(sK20(powerset(relation_rng(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_94]) ).
tcf(c_73673,plain,
! [X0: $i] :
( function(sK20(powerset(relation_rng(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_85]) ).
tcf(c_74549,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(X0))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_dom(X0))))) = sK14(sK1,sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_6419]) ).
tcf(c_74550,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(X0))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_dom(X0))))) = sK5(sK1,sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_5248]) ).
tcf(c_74551,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29434]) ).
tcf(c_74552,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29433]) ).
tcf(c_74553,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29432]) ).
tcf(c_74554,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29048]) ).
tcf(c_74555,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29047]) ).
tcf(c_74556,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29046]) ).
tcf(c_74557,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29001]) ).
tcf(c_74558,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_29000]) ).
tcf(c_74559,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_28999]) ).
tcf(c_74560,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(relation_dom(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12147]) ).
tcf(c_74561,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3853]) ).
tcf(c_74562,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3852]) ).
tcf(c_74563,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3847]) ).
tcf(c_74564,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3813]) ).
tcf(c_74565,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3812]) ).
tcf(c_74566,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3807]) ).
tcf(c_74567,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_39387]) ).
tcf(c_74568,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_39386]) ).
tcf(c_74569,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_39385]) ).
tcf(c_74570,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34275]) ).
tcf(c_74571,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34274]) ).
tcf(c_74572,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34273]) ).
tcf(c_74573,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34257]) ).
tcf(c_74574,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34256]) ).
tcf(c_74575,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_34255]) ).
tcf(c_74576,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_27401]) ).
tcf(c_74577,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_27400]) ).
tcf(c_74578,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_27399]) ).
tcf(c_74579,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25347]) ).
tcf(c_74580,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25346]) ).
tcf(c_74581,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25345]) ).
tcf(c_74582,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25312]) ).
tcf(c_74583,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25311]) ).
tcf(c_74584,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25310]) ).
tcf(c_74585,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25248]) ).
tcf(c_74586,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25247]) ).
tcf(c_74587,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25246]) ).
tcf(c_74588,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24512]) ).
tcf(c_74589,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24511]) ).
tcf(c_74590,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24510]) ).
tcf(c_74591,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24398]) ).
tcf(c_74592,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24397]) ).
tcf(c_74593,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24396]) ).
tcf(c_74594,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24361]) ).
tcf(c_74595,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24360]) ).
tcf(c_74596,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24359]) ).
tcf(c_74597,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24299]) ).
tcf(c_74598,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24298]) ).
tcf(c_74599,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24297]) ).
tcf(c_74600,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23557]) ).
tcf(c_74601,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23556]) ).
tcf(c_74602,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23555]) ).
tcf(c_74603,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23520]) ).
tcf(c_74604,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23519]) ).
tcf(c_74605,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23518]) ).
tcf(c_74606,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23406]) ).
tcf(c_74607,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23405]) ).
tcf(c_74608,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23404]) ).
tcf(c_74609,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23371]) ).
tcf(c_74610,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23370]) ).
tcf(c_74611,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23369]) ).
tcf(c_74612,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_22305]) ).
tcf(c_74613,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_22304]) ).
tcf(c_74614,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_22303]) ).
tcf(c_74615,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_21079]) ).
tcf(c_74616,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_21078]) ).
tcf(c_74617,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_21077]) ).
tcf(c_74618,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20790]) ).
tcf(c_74619,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20789]) ).
tcf(c_74620,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20788]) ).
tcf(c_74621,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20733]) ).
tcf(c_74622,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20732]) ).
tcf(c_74623,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20731]) ).
tcf(c_74624,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14787]) ).
tcf(c_74625,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20567]) ).
tcf(c_74626,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20566]) ).
tcf(c_74627,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20565]) ).
tcf(c_74628,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19623]) ).
tcf(c_74629,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14242]) ).
tcf(c_74630,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14162]) ).
tcf(c_74631,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14077]) ).
tcf(c_74632,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12144]) ).
tcf(c_74633,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19622]) ).
tcf(c_74634,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19621]) ).
tcf(c_74635,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12143]) ).
tcf(c_74636,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12142]) ).
tcf(c_74637,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12141]) ).
tcf(c_74638,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12140]) ).
tcf(c_74639,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19044]) ).
tcf(c_74640,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19043]) ).
tcf(c_74641,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12139]) ).
tcf(c_74642,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19042]) ).
tcf(c_74643,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18986]) ).
tcf(c_74644,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18985]) ).
tcf(c_74645,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18984]) ).
tcf(c_74646,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_36589]) ).
tcf(c_74647,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18933]) ).
tcf(c_74648,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18932]) ).
tcf(c_74649,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18931]) ).
tcf(c_74650,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18887]) ).
tcf(c_74651,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18886]) ).
tcf(c_74652,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18885]) ).
tcf(c_74653,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18057]) ).
tcf(c_74654,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18056]) ).
tcf(c_74655,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18055]) ).
tcf(c_74656,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17694]) ).
tcf(c_74657,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17693]) ).
tcf(c_74658,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17692]) ).
tcf(c_74659,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17624]) ).
tcf(c_74660,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17623]) ).
tcf(c_74661,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17622]) ).
tcf(c_74662,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17580]) ).
tcf(c_74663,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17579]) ).
tcf(c_74664,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17578]) ).
tcf(c_74665,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17545]) ).
tcf(c_74666,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17544]) ).
tcf(c_74667,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17543]) ).
tcf(c_74668,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_16055]) ).
tcf(c_74669,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_16054]) ).
tcf(c_74670,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_16053]) ).
tcf(c_74671,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15952]) ).
tcf(c_74672,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15951]) ).
tcf(c_74673,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15950]) ).
tcf(c_74674,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15917]) ).
tcf(c_74675,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15916]) ).
tcf(c_74676,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15915]) ).
tcf(c_74677,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15880]) ).
tcf(c_74678,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15879]) ).
tcf(c_74679,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15878]) ).
tcf(c_74680,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12149]) ).
tcf(c_74681,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12148]) ).
tcf(c_74682,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))) = relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11026]) ).
tcf(c_74683,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(relation_dom(X0))))) = relation_inverse(relation_rng(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11025]) ).
tcf(c_74684,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(relation_dom(X0))))) = relation_inverse(relation_dom(sK20(powerset(relation_dom(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11024]) ).
tcf(c_74685,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3663]) ).
tcf(c_74686,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3662]) ).
tcf(c_74687,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(relation_dom(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3661]) ).
tcf(c_74688,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = relation_rng(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3632]) ).
tcf(c_74689,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_12146]) ).
tcf(c_74690,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = relation_inverse(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3631]) ).
tcf(c_74691,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = relation_dom(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_3626]) ).
tcf(c_74692,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14780]) ).
tcf(c_74693,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14779]) ).
tcf(c_74694,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14778]) ).
tcf(c_74695,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14235]) ).
tcf(c_74696,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14234]) ).
tcf(c_74697,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14233]) ).
tcf(c_74698,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14155]) ).
tcf(c_74699,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14154]) ).
tcf(c_74700,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14153]) ).
tcf(c_74701,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14070]) ).
tcf(c_74702,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14069]) ).
tcf(c_74703,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_14068]) ).
tcf(c_74704,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11811]) ).
tcf(c_74705,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11810]) ).
tcf(c_74706,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11809]) ).
tcf(c_74707,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11771]) ).
tcf(c_74708,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11770]) ).
tcf(c_74709,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11769]) ).
tcf(c_74710,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11729]) ).
tcf(c_74711,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11728]) ).
tcf(c_74712,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11727]) ).
tcf(c_74713,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11691]) ).
tcf(c_74714,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11690]) ).
tcf(c_74715,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11689]) ).
tcf(c_74716,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11660]) ).
tcf(c_74717,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11659]) ).
tcf(c_74718,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11658]) ).
tcf(c_74719,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11297]) ).
tcf(c_74720,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11296]) ).
tcf(c_74721,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_11295]) ).
tcf(c_74732,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(relation_dom(X0)))) = relation_inverse(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_957]) ).
tcf(c_74738,plain,
! [X0: $i] :
( relation(sK20(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_94]) ).
tcf(c_74739,plain,
! [X0: $i] :
( function(sK20(powerset(relation_dom(X0))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_85]) ).
tcf(c_75489,plain,
( relation(sK20(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3424,c_73672]) ).
tcf(c_75490,plain,
( relation(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_73672]) ).
tcf(c_75492,plain,
( relation(sK20(powerset(relation_dom(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_73672]) ).
tcf(c_75497,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(X0))))) = relation_dom(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73672,c_72]) ).
tcf(c_75498,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(X0))))) = relation_rng(sK20(powerset(relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73672,c_71]) ).
tcf(c_75499,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0))))) = sK20(powerset(relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73672,c_120]) ).
tcf(c_75500,plain,
( relation(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_75489,c_14781]) ).
tcf(c_75571,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4030,c_6475]) ).
tcf(c_75573,plain,
( in(sK24(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK2)),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_6475]) ).
tcf(c_75574,plain,
( in(sK24(sK1,relation_inverse(sK9)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK9)),relation_rng(sK9))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_6475]) ).
tcf(c_75575,plain,
( in(sK24(sK1,relation_inverse(sK10)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK10)),relation_rng(sK10))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_6475]) ).
tcf(c_75576,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_6475]) ).
tcf(c_75577,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK2),sK24(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6475,c_70]) ).
tcf(c_75578,plain,
! [X0: $i] :
( element(sK24(sK1,X0),relation_dom(sK2))
| in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_69]) ).
tcf(c_75581,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,X0))) = apply(sK1,sK15(sK1,sK24(sK1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_12335]) ).
tcf(c_75582,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,X0)))) = sK15(sK1,sK24(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_8396]) ).
tcf(c_75583,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,X0)))) = sK15(sK1,sK24(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_8395]) ).
tcf(c_75584,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_4044]) ).
tcf(c_75585,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,X0)) = apply(sK2,sK24(sK1,X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6475,c_42224]) ).
tcf(c_75586,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_12701]) ).
tcf(c_75587,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,X0))) = sK24(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_10144]) ).
tcf(c_75588,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,X0)) = sK15(sK1,sK24(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_4468]) ).
tcf(c_75589,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK23(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6475,c_70]) ).
tcf(c_75590,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| element(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6475,c_69]) ).
tcf(c_75591,plain,
! [X0: $i] :
( in(sK24(sK1,X0),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6475,c_67]) ).
tcf(c_75603,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_12335]) ).
tcf(c_75604,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_8396]) ).
tcf(c_75605,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_8395]) ).
tcf(c_75606,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_4044]) ).
tcf(c_75607,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6475,c_42224]) ).
tcf(c_75608,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_12701]) ).
tcf(c_75609,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_10144]) ).
tcf(c_75610,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6475,c_4468]) ).
tcf(c_75611,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_6475,c_68472]) ).
tcf(c_75614,plain,
( in(sK24(sK1,sK12),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75611,c_95]) ).
tcf(c_75638,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75576,c_3610]) ).
tcf(c_75654,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75571,c_3611]) ).
tcf(c_75658,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75610,c_61]) ).
tcf(c_75662,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75609,c_61]) ).
tcf(c_75666,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75608,c_61]) ).
tcf(c_75682,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75607,c_61]) ).
tcf(c_75687,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75606,c_61]) ).
tcf(c_75692,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75605,c_61]) ).
tcf(c_75696,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75604,c_61]) ).
tcf(c_75700,plain,
( in(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_75603,c_61]) ).
tcf(c_75791,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75658,c_70]) ).
tcf(c_75792,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75658,c_69]) ).
tcf(c_75795,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75658,c_12335]) ).
tcf(c_75796,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75658,c_8396]) ).
tcf(c_75797,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75658,c_8395]) ).
tcf(c_75798,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75658,c_4044]) ).
tcf(c_75799,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75658,c_42224]) ).
tcf(c_75800,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75658,c_12701]) ).
tcf(c_75801,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75658,c_10144]) ).
tcf(c_75802,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75658,c_4468]) ).
tcf(c_75841,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75662,c_70]) ).
tcf(c_75842,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_69]) ).
tcf(c_75845,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_12335]) ).
tcf(c_75846,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75662,c_8396]) ).
tcf(c_75847,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75662,c_8395]) ).
tcf(c_75848,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_4044]) ).
tcf(c_75849,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75662,c_42224]) ).
tcf(c_75850,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_12701]) ).
tcf(c_75851,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_10144]) ).
tcf(c_75852,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75662,c_4468]) ).
tcf(c_75959,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75666,c_70]) ).
tcf(c_75960,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_69]) ).
tcf(c_75963,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_12335]) ).
tcf(c_75964,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75666,c_8396]) ).
tcf(c_75965,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75666,c_8395]) ).
tcf(c_75966,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_4044]) ).
tcf(c_75967,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75666,c_42224]) ).
tcf(c_75968,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_12701]) ).
tcf(c_75969,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_10144]) ).
tcf(c_75970,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75666,c_4468]) ).
tcf(c_76011,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_70]) ).
tcf(c_76012,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_69]) ).
tcf(c_76015,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_12335]) ).
tcf(c_76016,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_8396]) ).
tcf(c_76017,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_8395]) ).
tcf(c_76018,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_4044]) ).
tcf(c_76019,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_42224]) ).
tcf(c_76020,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_12701]) ).
tcf(c_76021,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_10144]) ).
tcf(c_76022,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75682,c_4468]) ).
tcf(c_76100,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75687,c_70]) ).
tcf(c_76101,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75687,c_69]) ).
tcf(c_76104,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75687,c_12335]) ).
tcf(c_76105,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75687,c_8396]) ).
tcf(c_76106,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75687,c_8395]) ).
tcf(c_76107,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75687,c_4044]) ).
tcf(c_76108,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75687,c_42224]) ).
tcf(c_76109,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75687,c_12701]) ).
tcf(c_76110,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75687,c_10144]) ).
tcf(c_76111,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75687,c_4468]) ).
tcf(c_76159,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75692,c_70]) ).
tcf(c_76160,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_69]) ).
tcf(c_76163,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_12335]) ).
tcf(c_76164,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_8396]) ).
tcf(c_76165,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_8395]) ).
tcf(c_76166,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_4044]) ).
tcf(c_76167,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75692,c_42224]) ).
tcf(c_76168,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_12701]) ).
tcf(c_76169,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_10144]) ).
tcf(c_76170,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75692,c_4468]) ).
tcf(c_76473,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75696,c_70]) ).
tcf(c_76474,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_69]) ).
tcf(c_76477,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_12335]) ).
tcf(c_76478,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_8396]) ).
tcf(c_76479,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_8395]) ).
tcf(c_76480,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_4044]) ).
tcf(c_76481,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75696,c_42224]) ).
tcf(c_76482,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_12701]) ).
tcf(c_76483,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_10144]) ).
tcf(c_76484,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75696,c_4468]) ).
tcf(c_76553,plain,
( function(sK20(powerset(empty_set)))
| ~ empty(empty_set) ),
inference(superposition,[status(thm)],[c_3424,c_73673]) ).
tcf(c_76554,plain,
( function(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_73673]) ).
tcf(c_76556,plain,
( function(sK20(powerset(relation_dom(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_73673]) ).
tcf(c_76558,plain,
( function(empty_set)
| ~ empty(empty_set) ),
inference(light_normalisation,[status(thm)],[c_76553,c_14781]) ).
tcf(c_76570,plain,
( relation(sK20(powerset(relation_rng(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_74738]) ).
tcf(c_76572,plain,
( relation(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_74738]) ).
tcf(c_76576,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(X0))))) = relation_dom(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74738,c_72]) ).
tcf(c_76577,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(X0))))) = relation_rng(sK20(powerset(relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74738,c_71]) ).
tcf(c_76578,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0))))) = sK20(powerset(relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_74738,c_120]) ).
tcf(c_76596,plain,
( function(sK20(powerset(relation_rng(sK9))))
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_74739]) ).
tcf(c_76598,plain,
( function(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_74739]) ).
tcf(c_76607,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35022]) ).
tcf(c_76608,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35022]) ).
tcf(c_76609,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35022]) ).
tcf(c_76610,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35022]) ).
tcf(c_76611,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35022]) ).
tcf(c_76612,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35022]) ).
tcf(c_76613,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35022]) ).
tcf(c_76614,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35022]) ).
tcf(c_76635,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35022]) ).
tcf(c_76636,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(X0)))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(sK20(powerset(X0)))))) = sK14(sK1,sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_6419]) ).
tcf(c_76637,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(X0)))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(sK20(powerset(X0)))))) = sK5(sK1,sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_5248]) ).
tcf(c_76638,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29434]) ).
tcf(c_76639,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29433]) ).
tcf(c_76640,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29432]) ).
tcf(c_76641,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29048]) ).
tcf(c_76642,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29047]) ).
tcf(c_76643,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29046]) ).
tcf(c_76644,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29001]) ).
tcf(c_76645,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_29000]) ).
tcf(c_76646,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_28999]) ).
tcf(c_76647,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12147]) ).
tcf(c_76648,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3853]) ).
tcf(c_76649,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3852]) ).
tcf(c_76650,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3847]) ).
tcf(c_76651,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3813]) ).
tcf(c_76652,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3812]) ).
tcf(c_76653,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3807]) ).
tcf(c_76654,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_39387]) ).
tcf(c_76655,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_39386]) ).
tcf(c_76656,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_39385]) ).
tcf(c_76657,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34275]) ).
tcf(c_76658,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34274]) ).
tcf(c_76659,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34273]) ).
tcf(c_76660,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34257]) ).
tcf(c_76661,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34256]) ).
tcf(c_76662,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_34255]) ).
tcf(c_76663,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_27401]) ).
tcf(c_76664,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_27400]) ).
tcf(c_76665,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_27399]) ).
tcf(c_76666,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25347]) ).
tcf(c_76667,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25346]) ).
tcf(c_76668,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25345]) ).
tcf(c_76669,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25312]) ).
tcf(c_76670,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25311]) ).
tcf(c_76671,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25310]) ).
tcf(c_76672,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25248]) ).
tcf(c_76673,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25247]) ).
tcf(c_76674,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25246]) ).
tcf(c_76675,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24512]) ).
tcf(c_76676,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24511]) ).
tcf(c_76677,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24510]) ).
tcf(c_76678,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24398]) ).
tcf(c_76679,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24397]) ).
tcf(c_76680,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24396]) ).
tcf(c_76681,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24361]) ).
tcf(c_76682,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24360]) ).
tcf(c_76683,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24359]) ).
tcf(c_76684,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24299]) ).
tcf(c_76685,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24298]) ).
tcf(c_76686,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24297]) ).
tcf(c_76687,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23557]) ).
tcf(c_76688,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23556]) ).
tcf(c_76689,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23555]) ).
tcf(c_76690,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23520]) ).
tcf(c_76691,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23519]) ).
tcf(c_76692,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23518]) ).
tcf(c_76693,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23406]) ).
tcf(c_76694,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23405]) ).
tcf(c_76695,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23404]) ).
tcf(c_76696,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23371]) ).
tcf(c_76697,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23370]) ).
tcf(c_76698,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23369]) ).
tcf(c_76699,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_22305]) ).
tcf(c_76700,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_22304]) ).
tcf(c_76701,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_22303]) ).
tcf(c_76702,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_21079]) ).
tcf(c_76703,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_21078]) ).
tcf(c_76704,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_21077]) ).
tcf(c_76705,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20790]) ).
tcf(c_76706,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20789]) ).
tcf(c_76707,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20788]) ).
tcf(c_76708,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20733]) ).
tcf(c_76709,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20732]) ).
tcf(c_76710,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20731]) ).
tcf(c_76711,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14787]) ).
tcf(c_76712,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20567]) ).
tcf(c_76713,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20566]) ).
tcf(c_76714,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20565]) ).
tcf(c_76715,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19623]) ).
tcf(c_76716,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14242]) ).
tcf(c_76717,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14162]) ).
tcf(c_76718,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14077]) ).
tcf(c_76719,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12144]) ).
tcf(c_76720,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19622]) ).
tcf(c_76721,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19621]) ).
tcf(c_76722,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12143]) ).
tcf(c_76723,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12142]) ).
tcf(c_76724,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12141]) ).
tcf(c_76725,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12140]) ).
tcf(c_76726,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19044]) ).
tcf(c_76727,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19043]) ).
tcf(c_76728,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12139]) ).
tcf(c_76729,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19042]) ).
tcf(c_76730,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18986]) ).
tcf(c_76731,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18985]) ).
tcf(c_76732,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18984]) ).
tcf(c_76733,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_36589]) ).
tcf(c_76734,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18933]) ).
tcf(c_76735,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18932]) ).
tcf(c_76736,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18931]) ).
tcf(c_76737,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18887]) ).
tcf(c_76738,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18886]) ).
tcf(c_76739,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18885]) ).
tcf(c_76740,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18057]) ).
tcf(c_76741,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18056]) ).
tcf(c_76742,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18055]) ).
tcf(c_76743,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17694]) ).
tcf(c_76744,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17693]) ).
tcf(c_76745,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17692]) ).
tcf(c_76746,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17624]) ).
tcf(c_76747,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17623]) ).
tcf(c_76748,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17622]) ).
tcf(c_76749,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17580]) ).
tcf(c_76750,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17579]) ).
tcf(c_76751,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17578]) ).
tcf(c_76752,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17545]) ).
tcf(c_76753,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17544]) ).
tcf(c_76754,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17543]) ).
tcf(c_76755,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_16055]) ).
tcf(c_76756,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_16054]) ).
tcf(c_76757,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_16053]) ).
tcf(c_76758,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15952]) ).
tcf(c_76759,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15951]) ).
tcf(c_76760,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15950]) ).
tcf(c_76761,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15917]) ).
tcf(c_76762,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15916]) ).
tcf(c_76763,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15915]) ).
tcf(c_76764,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15880]) ).
tcf(c_76765,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15879]) ).
tcf(c_76766,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15878]) ).
tcf(c_76767,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12149]) ).
tcf(c_76768,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12148]) ).
tcf(c_76769,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11026]) ).
tcf(c_76770,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))) = relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11025]) ).
tcf(c_76771,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))) = relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11024]) ).
tcf(c_76772,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3663]) ).
tcf(c_76773,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3662]) ).
tcf(c_76774,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3661]) ).
tcf(c_76775,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = relation_rng(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3632]) ).
tcf(c_76776,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_12146]) ).
tcf(c_76777,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = relation_inverse(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3631]) ).
tcf(c_76778,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = relation_dom(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_3626]) ).
tcf(c_76779,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14780]) ).
tcf(c_76780,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14779]) ).
tcf(c_76781,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14778]) ).
tcf(c_76782,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14235]) ).
tcf(c_76783,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14234]) ).
tcf(c_76784,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14233]) ).
tcf(c_76785,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14155]) ).
tcf(c_76786,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14154]) ).
tcf(c_76787,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14153]) ).
tcf(c_76788,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14070]) ).
tcf(c_76789,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14069]) ).
tcf(c_76790,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_14068]) ).
tcf(c_76791,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11811]) ).
tcf(c_76792,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11810]) ).
tcf(c_76793,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11809]) ).
tcf(c_76794,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11771]) ).
tcf(c_76795,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11770]) ).
tcf(c_76796,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11769]) ).
tcf(c_76797,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11729]) ).
tcf(c_76798,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11728]) ).
tcf(c_76799,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11727]) ).
tcf(c_76800,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11691]) ).
tcf(c_76801,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11690]) ).
tcf(c_76802,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11689]) ).
tcf(c_76803,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11660]) ).
tcf(c_76804,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11659]) ).
tcf(c_76805,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11658]) ).
tcf(c_76806,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11297]) ).
tcf(c_76807,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11296]) ).
tcf(c_76808,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_11295]) ).
tcf(c_76819,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(sK20(powerset(X0))))) = relation_inverse(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_957]) ).
tcf(c_76825,plain,
! [X0: $i] :
( relation(sK20(powerset(sK20(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_94]) ).
tcf(c_76826,plain,
! [X0: $i] :
( function(sK20(powerset(sK20(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_85]) ).
tcf(c_77522,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35022]) ).
tcf(c_77523,plain,
( ( sK20(powerset(relation_rng(sK9))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_rng(sK9))))) = sK14(sK1,sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_6419]) ).
tcf(c_77524,plain,
( ( sK20(powerset(relation_rng(sK9))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_rng(sK9))))) = sK5(sK1,sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_5248]) ).
tcf(c_77525,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29434]) ).
tcf(c_77526,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29433]) ).
tcf(c_77527,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29432]) ).
tcf(c_77528,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29048]) ).
tcf(c_77529,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29047]) ).
tcf(c_77530,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29046]) ).
tcf(c_77531,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29001]) ).
tcf(c_77532,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_29000]) ).
tcf(c_77533,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_28999]) ).
tcf(c_77534,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_rng(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12147]) ).
tcf(c_77535,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3853]) ).
tcf(c_77536,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3852]) ).
tcf(c_77537,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3847]) ).
tcf(c_77538,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3813]) ).
tcf(c_77539,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3812]) ).
tcf(c_77540,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3807]) ).
tcf(c_77541,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_39387]) ).
tcf(c_77542,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_39386]) ).
tcf(c_77543,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_39385]) ).
tcf(c_77544,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34275]) ).
tcf(c_77545,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34274]) ).
tcf(c_77546,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34273]) ).
tcf(c_77547,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34257]) ).
tcf(c_77548,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34256]) ).
tcf(c_77549,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_34255]) ).
tcf(c_77550,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_27401]) ).
tcf(c_77551,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_27400]) ).
tcf(c_77552,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_27399]) ).
tcf(c_77553,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25347]) ).
tcf(c_77554,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25346]) ).
tcf(c_77555,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25345]) ).
tcf(c_77556,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25312]) ).
tcf(c_77557,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25311]) ).
tcf(c_77558,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25310]) ).
tcf(c_77559,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25248]) ).
tcf(c_77560,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25247]) ).
tcf(c_77561,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25246]) ).
tcf(c_77562,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24512]) ).
tcf(c_77563,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24511]) ).
tcf(c_77564,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24510]) ).
tcf(c_77565,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24398]) ).
tcf(c_77566,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24397]) ).
tcf(c_77567,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24396]) ).
tcf(c_77568,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24361]) ).
tcf(c_77569,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24360]) ).
tcf(c_77570,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24359]) ).
tcf(c_77571,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24299]) ).
tcf(c_77572,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24298]) ).
tcf(c_77573,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24297]) ).
tcf(c_77574,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23557]) ).
tcf(c_77575,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23556]) ).
tcf(c_77576,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23555]) ).
tcf(c_77577,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23520]) ).
tcf(c_77578,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23519]) ).
tcf(c_77579,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23518]) ).
tcf(c_77580,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23406]) ).
tcf(c_77581,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23405]) ).
tcf(c_77582,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23404]) ).
tcf(c_77583,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23371]) ).
tcf(c_77584,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23370]) ).
tcf(c_77585,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23369]) ).
tcf(c_77586,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_22305]) ).
tcf(c_77587,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_22304]) ).
tcf(c_77588,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_22303]) ).
tcf(c_77589,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_21079]) ).
tcf(c_77590,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_21078]) ).
tcf(c_77591,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_21077]) ).
tcf(c_77592,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20790]) ).
tcf(c_77593,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20789]) ).
tcf(c_77594,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20788]) ).
tcf(c_77595,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20733]) ).
tcf(c_77596,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20732]) ).
tcf(c_77597,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20731]) ).
tcf(c_77598,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14787]) ).
tcf(c_77599,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20567]) ).
tcf(c_77600,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20566]) ).
tcf(c_77601,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20565]) ).
tcf(c_77602,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19623]) ).
tcf(c_77603,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14242]) ).
tcf(c_77604,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14162]) ).
tcf(c_77605,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14077]) ).
tcf(c_77606,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12144]) ).
tcf(c_77607,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19622]) ).
tcf(c_77608,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19621]) ).
tcf(c_77609,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12143]) ).
tcf(c_77610,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12142]) ).
tcf(c_77611,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12141]) ).
tcf(c_77612,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12140]) ).
tcf(c_77613,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19044]) ).
tcf(c_77614,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19043]) ).
tcf(c_77615,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12139]) ).
tcf(c_77616,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19042]) ).
tcf(c_77617,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18986]) ).
tcf(c_77618,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18985]) ).
tcf(c_77619,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18984]) ).
tcf(c_77620,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_36589]) ).
tcf(c_77621,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18933]) ).
tcf(c_77622,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18932]) ).
tcf(c_77623,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18931]) ).
tcf(c_77624,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18887]) ).
tcf(c_77625,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18886]) ).
tcf(c_77626,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18885]) ).
tcf(c_77627,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18057]) ).
tcf(c_77628,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18056]) ).
tcf(c_77629,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18055]) ).
tcf(c_77630,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17694]) ).
tcf(c_77631,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17693]) ).
tcf(c_77632,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17692]) ).
tcf(c_77633,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17624]) ).
tcf(c_77634,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17623]) ).
tcf(c_77635,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17622]) ).
tcf(c_77636,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17580]) ).
tcf(c_77637,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17579]) ).
tcf(c_77638,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17578]) ).
tcf(c_77639,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17545]) ).
tcf(c_77640,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17544]) ).
tcf(c_77641,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17543]) ).
tcf(c_77642,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_16055]) ).
tcf(c_77643,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_16054]) ).
tcf(c_77644,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_16053]) ).
tcf(c_77645,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15952]) ).
tcf(c_77646,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15951]) ).
tcf(c_77647,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15950]) ).
tcf(c_77648,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15917]) ).
tcf(c_77649,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15916]) ).
tcf(c_77650,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15915]) ).
tcf(c_77651,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15880]) ).
tcf(c_77652,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15879]) ).
tcf(c_77653,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15878]) ).
tcf(c_77654,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12149]) ).
tcf(c_77655,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12148]) ).
tcf(c_77656,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))) = relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11026]) ).
tcf(c_77657,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))) = relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11025]) ).
tcf(c_77658,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))) = relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11024]) ).
tcf(c_77659,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3663]) ).
tcf(c_77660,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3662]) ).
tcf(c_77661,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3661]) ).
tcf(c_77662,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = relation_rng(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3632]) ).
tcf(c_77663,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12146]) ).
tcf(c_77664,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = relation_inverse(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3631]) ).
tcf(c_77665,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = relation_dom(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3626]) ).
tcf(c_77666,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14780]) ).
tcf(c_77667,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14779]) ).
tcf(c_77668,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14778]) ).
tcf(c_77669,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14235]) ).
tcf(c_77670,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14234]) ).
tcf(c_77671,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14233]) ).
tcf(c_77672,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14155]) ).
tcf(c_77673,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14154]) ).
tcf(c_77674,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14153]) ).
tcf(c_77675,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14070]) ).
tcf(c_77676,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14069]) ).
tcf(c_77677,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_14068]) ).
tcf(c_77678,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11811]) ).
tcf(c_77679,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11810]) ).
tcf(c_77680,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11809]) ).
tcf(c_77681,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11771]) ).
tcf(c_77682,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11770]) ).
tcf(c_77683,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11769]) ).
tcf(c_77684,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11729]) ).
tcf(c_77685,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11728]) ).
tcf(c_77686,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11727]) ).
tcf(c_77687,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11691]) ).
tcf(c_77688,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11690]) ).
tcf(c_77689,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11689]) ).
tcf(c_77690,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11660]) ).
tcf(c_77691,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11659]) ).
tcf(c_77692,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11658]) ).
tcf(c_77693,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11297]) ).
tcf(c_77694,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11296]) ).
tcf(c_77695,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_11295]) ).
tcf(c_77696,plain,
( ( sK20(powerset(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_12150]) ).
tcf(c_77697,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_9831]) ).
tcf(c_77698,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_9830]) ).
tcf(c_77699,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_9829]) ).
tcf(c_77700,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3423]) ).
tcf(c_77701,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3422]) ).
tcf(c_77702,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3421]) ).
tcf(c_77703,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3403]) ).
tcf(c_77704,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3402]) ).
tcf(c_77705,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3401]) ).
tcf(c_77706,plain,
( ( function_inverse(sK20(powerset(relation_rng(sK9)))) = relation_inverse(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_957]) ).
tcf(c_77707,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3333]) ).
tcf(c_77708,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK9))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_66]) ).
tcf(c_77709,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3330]) ).
tcf(c_77710,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_3327]) ).
tcf(c_77711,plain,
( ( sK20(powerset(relation_rng(sK9))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_133]) ).
tcf(c_78670,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35022]) ).
tcf(c_78671,plain,
( ( sK20(powerset(relation_rng(sK12))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_rng(sK12))))) = sK14(sK1,sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_6419]) ).
tcf(c_78672,plain,
( ( sK20(powerset(relation_rng(sK12))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_rng(sK12))))) = sK5(sK1,sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_5248]) ).
tcf(c_78673,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29434]) ).
tcf(c_78674,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29433]) ).
tcf(c_78675,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29432]) ).
tcf(c_78676,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29048]) ).
tcf(c_78677,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29047]) ).
tcf(c_78678,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29046]) ).
tcf(c_78679,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29001]) ).
tcf(c_78680,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_29000]) ).
tcf(c_78681,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_28999]) ).
tcf(c_78682,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12147]) ).
tcf(c_78683,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3853]) ).
tcf(c_78684,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3852]) ).
tcf(c_78685,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3847]) ).
tcf(c_78686,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3813]) ).
tcf(c_78687,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3812]) ).
tcf(c_78688,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3807]) ).
tcf(c_78689,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_39387]) ).
tcf(c_78690,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_39386]) ).
tcf(c_78691,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_39385]) ).
tcf(c_78692,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34275]) ).
tcf(c_78693,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34274]) ).
tcf(c_78694,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34273]) ).
tcf(c_78695,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34257]) ).
tcf(c_78696,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34256]) ).
tcf(c_78697,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_34255]) ).
tcf(c_78698,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_27401]) ).
tcf(c_78699,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_27400]) ).
tcf(c_78700,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_27399]) ).
tcf(c_78701,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25347]) ).
tcf(c_78702,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25346]) ).
tcf(c_78703,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25345]) ).
tcf(c_78704,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25312]) ).
tcf(c_78705,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25311]) ).
tcf(c_78706,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25310]) ).
tcf(c_78707,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25248]) ).
tcf(c_78708,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25247]) ).
tcf(c_78709,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25246]) ).
tcf(c_78710,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24512]) ).
tcf(c_78711,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24511]) ).
tcf(c_78712,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24510]) ).
tcf(c_78713,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24398]) ).
tcf(c_78714,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24397]) ).
tcf(c_78715,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24396]) ).
tcf(c_78716,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24361]) ).
tcf(c_78717,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24360]) ).
tcf(c_78718,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24359]) ).
tcf(c_78719,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24299]) ).
tcf(c_78720,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24298]) ).
tcf(c_78721,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24297]) ).
tcf(c_78722,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23557]) ).
tcf(c_78723,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23556]) ).
tcf(c_78724,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23555]) ).
tcf(c_78725,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23520]) ).
tcf(c_78726,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23519]) ).
tcf(c_78727,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23518]) ).
tcf(c_78728,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23406]) ).
tcf(c_78729,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23405]) ).
tcf(c_78730,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23404]) ).
tcf(c_78731,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23371]) ).
tcf(c_78732,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23370]) ).
tcf(c_78733,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23369]) ).
tcf(c_78734,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_22305]) ).
tcf(c_78735,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_22304]) ).
tcf(c_78736,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_22303]) ).
tcf(c_78737,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_21079]) ).
tcf(c_78738,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_21078]) ).
tcf(c_78739,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_21077]) ).
tcf(c_78740,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20790]) ).
tcf(c_78741,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20789]) ).
tcf(c_78742,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20788]) ).
tcf(c_78743,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20733]) ).
tcf(c_78744,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20732]) ).
tcf(c_78745,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20731]) ).
tcf(c_78746,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14787]) ).
tcf(c_78747,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20567]) ).
tcf(c_78748,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20566]) ).
tcf(c_78749,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20565]) ).
tcf(c_78750,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19623]) ).
tcf(c_78751,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14242]) ).
tcf(c_78752,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14162]) ).
tcf(c_78753,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14077]) ).
tcf(c_78754,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12144]) ).
tcf(c_78755,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19622]) ).
tcf(c_78756,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19621]) ).
tcf(c_78757,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12143]) ).
tcf(c_78758,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12142]) ).
tcf(c_78759,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12141]) ).
tcf(c_78760,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12140]) ).
tcf(c_78761,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19044]) ).
tcf(c_78762,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19043]) ).
tcf(c_78763,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12139]) ).
tcf(c_78764,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19042]) ).
tcf(c_78765,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18986]) ).
tcf(c_78766,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18985]) ).
tcf(c_78767,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18984]) ).
tcf(c_78768,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_36589]) ).
tcf(c_78769,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18933]) ).
tcf(c_78770,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18932]) ).
tcf(c_78771,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18931]) ).
tcf(c_78772,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18887]) ).
tcf(c_78773,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18886]) ).
tcf(c_78774,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18885]) ).
tcf(c_78775,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18057]) ).
tcf(c_78776,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18056]) ).
tcf(c_78777,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18055]) ).
tcf(c_78778,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17694]) ).
tcf(c_78779,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17693]) ).
tcf(c_78780,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17692]) ).
tcf(c_78781,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17624]) ).
tcf(c_78782,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17623]) ).
tcf(c_78783,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17622]) ).
tcf(c_78784,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17580]) ).
tcf(c_78785,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17579]) ).
tcf(c_78786,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17578]) ).
tcf(c_78787,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17545]) ).
tcf(c_78788,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17544]) ).
tcf(c_78789,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17543]) ).
tcf(c_78790,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_16055]) ).
tcf(c_78791,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_16054]) ).
tcf(c_78792,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_16053]) ).
tcf(c_78793,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15952]) ).
tcf(c_78794,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15951]) ).
tcf(c_78795,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15950]) ).
tcf(c_78796,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15917]) ).
tcf(c_78797,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15916]) ).
tcf(c_78798,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15915]) ).
tcf(c_78799,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15880]) ).
tcf(c_78800,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15879]) ).
tcf(c_78801,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15878]) ).
tcf(c_78802,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12149]) ).
tcf(c_78803,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12148]) ).
tcf(c_78804,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11026]) ).
tcf(c_78805,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11025]) ).
tcf(c_78806,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11024]) ).
tcf(c_78807,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3663]) ).
tcf(c_78808,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3662]) ).
tcf(c_78809,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3661]) ).
tcf(c_78810,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_rng(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3632]) ).
tcf(c_78811,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12146]) ).
tcf(c_78812,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_inverse(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3631]) ).
tcf(c_78813,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_dom(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3626]) ).
tcf(c_78814,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14780]) ).
tcf(c_78815,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14779]) ).
tcf(c_78816,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14778]) ).
tcf(c_78817,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14235]) ).
tcf(c_78818,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14234]) ).
tcf(c_78819,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14233]) ).
tcf(c_78820,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14155]) ).
tcf(c_78821,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14154]) ).
tcf(c_78822,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14153]) ).
tcf(c_78823,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14070]) ).
tcf(c_78824,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14069]) ).
tcf(c_78825,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_14068]) ).
tcf(c_78826,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11811]) ).
tcf(c_78827,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11810]) ).
tcf(c_78828,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11809]) ).
tcf(c_78829,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11771]) ).
tcf(c_78830,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11770]) ).
tcf(c_78831,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11769]) ).
tcf(c_78832,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11729]) ).
tcf(c_78833,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11728]) ).
tcf(c_78834,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11727]) ).
tcf(c_78835,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11691]) ).
tcf(c_78836,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11690]) ).
tcf(c_78837,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11689]) ).
tcf(c_78838,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11660]) ).
tcf(c_78839,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11659]) ).
tcf(c_78840,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11658]) ).
tcf(c_78841,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11297]) ).
tcf(c_78842,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11296]) ).
tcf(c_78843,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_11295]) ).
tcf(c_78844,plain,
( ( sK20(powerset(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_12150]) ).
tcf(c_78845,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_9831]) ).
tcf(c_78846,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_9830]) ).
tcf(c_78847,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_9829]) ).
tcf(c_78848,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3423]) ).
tcf(c_78849,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3422]) ).
tcf(c_78850,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3421]) ).
tcf(c_78851,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3403]) ).
tcf(c_78852,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3402]) ).
tcf(c_78853,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3401]) ).
tcf(c_78854,plain,
( ( function_inverse(sK20(powerset(relation_rng(sK12)))) = relation_inverse(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_957]) ).
tcf(c_78855,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3333]) ).
tcf(c_78856,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK12))) = X0 )
| ~ empty(X0)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_66]) ).
tcf(c_78857,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3330]) ).
tcf(c_78858,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_3327]) ).
tcf(c_78859,plain,
( ( sK20(powerset(relation_rng(sK12))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_133]) ).
tcf(c_78860,plain,
( relation(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_94]) ).
tcf(c_78861,plain,
( function(sK20(powerset(relation_rng(sK12))))
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_85]) ).
tcf(c_79692,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35022]) ).
tcf(c_79693,plain,
( ( sK20(powerset(relation_rng(sK12))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_rng(sK12))))) = sK14(sK1,sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_6419]) ).
tcf(c_79694,plain,
( ( sK20(powerset(relation_rng(sK12))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_rng(sK12))))) = sK5(sK1,sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_5248]) ).
tcf(c_79695,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29434]) ).
tcf(c_79696,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29433]) ).
tcf(c_79697,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29432]) ).
tcf(c_79698,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29048]) ).
tcf(c_79699,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29047]) ).
tcf(c_79700,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29046]) ).
tcf(c_79701,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29001]) ).
tcf(c_79702,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_29000]) ).
tcf(c_79703,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_28999]) ).
tcf(c_79704,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_rng(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12147]) ).
tcf(c_79705,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3853]) ).
tcf(c_79706,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3852]) ).
tcf(c_79707,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3847]) ).
tcf(c_79708,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3813]) ).
tcf(c_79709,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3812]) ).
tcf(c_79710,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3807]) ).
tcf(c_79711,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_39387]) ).
tcf(c_79712,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_39386]) ).
tcf(c_79713,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_39385]) ).
tcf(c_79714,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34275]) ).
tcf(c_79715,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34274]) ).
tcf(c_79716,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34273]) ).
tcf(c_79717,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34257]) ).
tcf(c_79718,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34256]) ).
tcf(c_79719,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_34255]) ).
tcf(c_79720,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_27401]) ).
tcf(c_79721,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_27400]) ).
tcf(c_79722,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_27399]) ).
tcf(c_79723,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25347]) ).
tcf(c_79724,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25346]) ).
tcf(c_79725,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25345]) ).
tcf(c_79726,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25312]) ).
tcf(c_79727,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25311]) ).
tcf(c_79728,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25310]) ).
tcf(c_79729,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25248]) ).
tcf(c_79730,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25247]) ).
tcf(c_79731,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25246]) ).
tcf(c_79732,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24512]) ).
tcf(c_79733,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24511]) ).
tcf(c_79734,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24510]) ).
tcf(c_79735,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24398]) ).
tcf(c_79736,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24397]) ).
tcf(c_79737,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24396]) ).
tcf(c_79738,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24361]) ).
tcf(c_79739,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24360]) ).
tcf(c_79740,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24359]) ).
tcf(c_79741,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24299]) ).
tcf(c_79742,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24298]) ).
tcf(c_79743,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24297]) ).
tcf(c_79744,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23557]) ).
tcf(c_79745,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23556]) ).
tcf(c_79746,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23555]) ).
tcf(c_79747,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23520]) ).
tcf(c_79748,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23519]) ).
tcf(c_79749,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23518]) ).
tcf(c_79750,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23406]) ).
tcf(c_79751,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23405]) ).
tcf(c_79752,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23404]) ).
tcf(c_79753,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23371]) ).
tcf(c_79754,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23370]) ).
tcf(c_79755,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23369]) ).
tcf(c_79756,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_22305]) ).
tcf(c_79757,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_22304]) ).
tcf(c_79758,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_22303]) ).
tcf(c_79759,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_21079]) ).
tcf(c_79760,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_21078]) ).
tcf(c_79761,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_21077]) ).
tcf(c_79762,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20790]) ).
tcf(c_79763,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20789]) ).
tcf(c_79764,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20788]) ).
tcf(c_79765,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20733]) ).
tcf(c_79766,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20732]) ).
tcf(c_79767,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20731]) ).
tcf(c_79768,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14787]) ).
tcf(c_79769,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20567]) ).
tcf(c_79770,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20566]) ).
tcf(c_79771,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20565]) ).
tcf(c_79772,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19623]) ).
tcf(c_79773,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14242]) ).
tcf(c_79774,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14162]) ).
tcf(c_79775,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14077]) ).
tcf(c_79776,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12144]) ).
tcf(c_79777,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19622]) ).
tcf(c_79778,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19621]) ).
tcf(c_79779,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12143]) ).
tcf(c_79780,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12142]) ).
tcf(c_79781,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12141]) ).
tcf(c_79782,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12140]) ).
tcf(c_79783,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19044]) ).
tcf(c_79784,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19043]) ).
tcf(c_79785,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12139]) ).
tcf(c_79786,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19042]) ).
tcf(c_79787,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18986]) ).
tcf(c_79788,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18985]) ).
tcf(c_79789,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18984]) ).
tcf(c_79790,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_36589]) ).
tcf(c_79791,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18933]) ).
tcf(c_79792,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18932]) ).
tcf(c_79793,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18931]) ).
tcf(c_79794,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18887]) ).
tcf(c_79795,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18886]) ).
tcf(c_79796,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18885]) ).
tcf(c_79797,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18057]) ).
tcf(c_79798,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18056]) ).
tcf(c_79799,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18055]) ).
tcf(c_79800,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17694]) ).
tcf(c_79801,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17693]) ).
tcf(c_79802,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17692]) ).
tcf(c_79803,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17624]) ).
tcf(c_79804,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17623]) ).
tcf(c_79805,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17622]) ).
tcf(c_79806,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17580]) ).
tcf(c_79807,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17579]) ).
tcf(c_79808,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17578]) ).
tcf(c_79809,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17545]) ).
tcf(c_79810,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17544]) ).
tcf(c_79811,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17543]) ).
tcf(c_79812,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_16055]) ).
tcf(c_79813,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_16054]) ).
tcf(c_79814,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_16053]) ).
tcf(c_79815,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15952]) ).
tcf(c_79816,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15951]) ).
tcf(c_79817,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15950]) ).
tcf(c_79818,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15917]) ).
tcf(c_79819,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15916]) ).
tcf(c_79820,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15915]) ).
tcf(c_79821,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15880]) ).
tcf(c_79822,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15879]) ).
tcf(c_79823,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15878]) ).
tcf(c_79824,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12149]) ).
tcf(c_79825,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12148]) ).
tcf(c_79826,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11026]) ).
tcf(c_79827,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11025]) ).
tcf(c_79828,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11024]) ).
tcf(c_79829,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3663]) ).
tcf(c_79830,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3662]) ).
tcf(c_79831,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3661]) ).
tcf(c_79832,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = relation_rng(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3632]) ).
tcf(c_79833,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12146]) ).
tcf(c_79834,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = relation_inverse(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3631]) ).
tcf(c_79835,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = relation_dom(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3626]) ).
tcf(c_79836,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14780]) ).
tcf(c_79837,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14779]) ).
tcf(c_79838,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14778]) ).
tcf(c_79839,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14235]) ).
tcf(c_79840,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14234]) ).
tcf(c_79841,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14233]) ).
tcf(c_79842,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14155]) ).
tcf(c_79843,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14154]) ).
tcf(c_79844,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14153]) ).
tcf(c_79845,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14070]) ).
tcf(c_79846,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14069]) ).
tcf(c_79847,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_14068]) ).
tcf(c_79848,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11811]) ).
tcf(c_79849,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11810]) ).
tcf(c_79850,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11809]) ).
tcf(c_79851,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11771]) ).
tcf(c_79852,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11770]) ).
tcf(c_79853,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11769]) ).
tcf(c_79854,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11729]) ).
tcf(c_79855,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11728]) ).
tcf(c_79856,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11727]) ).
tcf(c_79857,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11691]) ).
tcf(c_79858,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11690]) ).
tcf(c_79859,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11689]) ).
tcf(c_79860,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11660]) ).
tcf(c_79861,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11659]) ).
tcf(c_79862,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11658]) ).
tcf(c_79863,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11297]) ).
tcf(c_79864,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11296]) ).
tcf(c_79865,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_11295]) ).
tcf(c_79866,plain,
( ( sK20(powerset(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_12150]) ).
tcf(c_79867,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_9831]) ).
tcf(c_79868,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_9830]) ).
tcf(c_79869,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_9829]) ).
tcf(c_79870,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3423]) ).
tcf(c_79871,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3422]) ).
tcf(c_79872,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3421]) ).
tcf(c_79873,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3403]) ).
tcf(c_79874,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3402]) ).
tcf(c_79875,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_rng(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3401]) ).
tcf(c_79876,plain,
( ( function_inverse(sK20(powerset(relation_rng(sK12)))) = relation_inverse(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_957]) ).
tcf(c_79877,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3333]) ).
tcf(c_79878,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK12))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_66]) ).
tcf(c_79879,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3330]) ).
tcf(c_79880,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_3327]) ).
tcf(c_79881,plain,
( ( sK20(powerset(relation_rng(sK12))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_133]) ).
tcf(c_80600,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ in(relation_dom(sK2),sK24(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_75700,c_70]) ).
tcf(c_80601,plain,
( element(sK24(sK1,sK2),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75700,c_69]) ).
tcf(c_80604,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,sK2))) = apply(sK1,sK15(sK1,sK24(sK1,sK2))) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75700,c_12335]) ).
tcf(c_80605,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75700,c_8396]) ).
tcf(c_80606,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,sK2)))) = sK15(sK1,sK24(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_75700,c_8395]) ).
tcf(c_80607,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75700,c_4044]) ).
tcf(c_80608,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK1,sK2)) = apply(sK2,sK24(sK1,sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75700,c_42224]) ).
tcf(c_80609,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75700,c_12701]) ).
tcf(c_80610,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,sK2))) = sK24(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_75700,c_10144]) ).
tcf(c_80611,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK2)) = sK15(sK1,sK24(sK1,sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_75700,c_4468]) ).
tcf(c_80680,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_6564]) ).
tcf(c_80682,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_6564]) ).
tcf(c_80683,plain,
( in(sK24(relation_inverse(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_6564]) ).
tcf(c_80684,plain,
( in(sK24(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK24(relation_inverse(sK9),sK1),relation_dom(sK2))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_6564]) ).
tcf(c_80685,plain,
( in(sK24(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK24(relation_inverse(sK10),sK1),relation_dom(sK2))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_6564]) ).
tcf(c_80687,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK24(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6564,c_70]) ).
tcf(c_80688,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| element(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6564,c_69]) ).
tcf(c_80689,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6564,c_67]) ).
tcf(c_80690,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6564,c_43161]) ).
tcf(c_80691,plain,
( in(sK24(sK9,sK1),relation_dom(sK2))
| ( sK1 = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6564,c_29938]) ).
tcf(c_80692,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_6564,c_69454]) ).
tcf(c_80697,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80692,c_95]) ).
tcf(c_80701,plain,
( in(sK24(sK9,sK1),relation_dom(sK2))
| ( sK1 = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80691,c_83]) ).
tcf(c_80725,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80682,c_3610]) ).
tcf(c_80729,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80680,c_3611]) ).
tcf(c_80806,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(relation_inverse(sK2),sK1)) ),
inference(superposition,[status(thm)],[c_80683,c_70]) ).
tcf(c_80807,plain,
( element(sK24(relation_inverse(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_69]) ).
tcf(c_80810,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(relation_inverse(sK2),sK1))) = apply(sK1,sK15(sK1,sK24(relation_inverse(sK2),sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_12335]) ).
tcf(c_80811,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(relation_inverse(sK2),sK1)))) = sK15(sK1,sK24(relation_inverse(sK2),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_8396]) ).
tcf(c_80812,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(relation_inverse(sK2),sK1)))) = sK15(sK1,sK24(relation_inverse(sK2),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_8395]) ).
tcf(c_80813,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(relation_inverse(sK2),sK1))) = sK24(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_4044]) ).
tcf(c_80814,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(relation_inverse(sK2),sK1)) = apply(sK2,sK24(relation_inverse(sK2),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_42224]) ).
tcf(c_80815,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(relation_inverse(sK2),sK1))) = sK24(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_12701]) ).
tcf(c_80816,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(relation_inverse(sK2),sK1))) = sK24(relation_inverse(sK2),sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_10144]) ).
tcf(c_80817,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK2),sK1)) = sK15(sK1,sK24(relation_inverse(sK2),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80683,c_4468]) ).
tcf(c_80857,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4030,c_6565]) ).
tcf(c_80859,plain,
( in(sK24(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_6565]) ).
tcf(c_80860,plain,
( in(sK24(relation_inverse(sK9),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_6565]) ).
tcf(c_80861,plain,
( in(sK24(relation_inverse(sK10),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_6565]) ).
tcf(c_80862,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_6565]) ).
tcf(c_80863,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK2),sK24(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6565,c_70]) ).
tcf(c_80864,plain,
! [X0: $i] :
( element(sK24(X0,sK1),relation_dom(sK2))
| in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_69]) ).
tcf(c_80867,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(X0,sK1))) = apply(sK1,sK15(sK1,sK24(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_12335]) ).
tcf(c_80868,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(X0,sK1)))) = sK15(sK1,sK24(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_8396]) ).
tcf(c_80869,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(X0,sK1)))) = sK15(sK1,sK24(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_8395]) ).
tcf(c_80870,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_4044]) ).
tcf(c_80871,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK2),sK24(X0,sK1)) = apply(sK2,sK24(X0,sK1)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6565,c_42224]) ).
tcf(c_80872,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_12701]) ).
tcf(c_80873,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(X0,sK1))) = sK24(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_10144]) ).
tcf(c_80874,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK24(X0,sK1)) = sK15(sK1,sK24(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_4468]) ).
tcf(c_80875,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK23(X0,sK1)) ),
inference(superposition,[status(thm)],[c_6565,c_70]) ).
tcf(c_80876,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| element(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6565,c_69]) ).
tcf(c_80877,plain,
! [X0: $i] :
( in(sK24(X0,sK1),relation_dom(sK2))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6565,c_67]) ).
tcf(c_80889,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_12335]) ).
tcf(c_80890,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_8396]) ).
tcf(c_80891,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_8395]) ).
tcf(c_80892,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_4044]) ).
tcf(c_80893,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6565,c_42224]) ).
tcf(c_80894,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_12701]) ).
tcf(c_80895,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_10144]) ).
tcf(c_80896,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_6565,c_4468]) ).
tcf(c_80897,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_6565,c_68472]) ).
tcf(c_80900,plain,
( in(sK24(sK12,sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80897,c_95]) ).
tcf(c_80924,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80862,c_3610]) ).
tcf(c_80940,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80857,c_3611]) ).
tcf(c_80944,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80896,c_61]) ).
tcf(c_80948,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80895,c_61]) ).
tcf(c_80952,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80894,c_61]) ).
tcf(c_80968,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80893,c_61]) ).
tcf(c_80973,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80892,c_61]) ).
tcf(c_80978,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80891,c_61]) ).
tcf(c_80982,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80890,c_61]) ).
tcf(c_80986,plain,
( in(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80889,c_61]) ).
tcf(c_81359,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80944,c_70]) ).
tcf(c_81360,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80944,c_69]) ).
tcf(c_81363,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80944,c_12335]) ).
tcf(c_81364,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80944,c_8396]) ).
tcf(c_81365,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80944,c_8395]) ).
tcf(c_81366,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80944,c_4044]) ).
tcf(c_81367,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80944,c_42224]) ).
tcf(c_81368,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80944,c_12701]) ).
tcf(c_81369,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80944,c_10144]) ).
tcf(c_81370,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80944,c_4468]) ).
tcf(c_81463,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80948,c_70]) ).
tcf(c_81464,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_69]) ).
tcf(c_81467,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_12335]) ).
tcf(c_81468,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80948,c_8396]) ).
tcf(c_81469,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80948,c_8395]) ).
tcf(c_81470,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_4044]) ).
tcf(c_81471,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80948,c_42224]) ).
tcf(c_81472,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_12701]) ).
tcf(c_81473,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_10144]) ).
tcf(c_81474,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80948,c_4468]) ).
tcf(c_81513,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80952,c_70]) ).
tcf(c_81514,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_69]) ).
tcf(c_81517,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_12335]) ).
tcf(c_81518,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80952,c_8396]) ).
tcf(c_81519,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80952,c_8395]) ).
tcf(c_81520,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_4044]) ).
tcf(c_81521,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80952,c_42224]) ).
tcf(c_81522,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_12701]) ).
tcf(c_81523,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_10144]) ).
tcf(c_81524,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80952,c_4468]) ).
tcf(c_81565,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80968,c_70]) ).
tcf(c_81566,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_69]) ).
tcf(c_81569,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_12335]) ).
tcf(c_81570,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_8396]) ).
tcf(c_81571,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_8395]) ).
tcf(c_81572,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_4044]) ).
tcf(c_81573,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_42224]) ).
tcf(c_81574,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_12701]) ).
tcf(c_81575,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_10144]) ).
tcf(c_81576,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80968,c_4468]) ).
tcf(c_81650,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_17971,c_87]) ).
tcf(c_81651,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17971,c_13473]) ).
tcf(c_81652,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17971,c_13472]) ).
tcf(c_81653,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_17971,c_34564]) ).
tcf(c_81654,plain,
( element(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_34565]) ).
tcf(c_81655,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_34571]) ).
tcf(c_81656,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_34529]) ).
tcf(c_81657,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_12764]) ).
tcf(c_81658,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_9713]) ).
tcf(c_81659,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17971,c_13488]) ).
tcf(c_81660,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_17971,c_12807]) ).
tcf(c_81661,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17971,c_4623]) ).
tcf(c_81662,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_17971,c_4763]) ).
tcf(c_81663,plain,
( in(ordered_pair(sK21(sK1,sK1),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17971,c_50582]) ).
tcf(c_81664,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_17971,c_12789]) ).
tcf(c_81719,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_81650,c_4030]) ).
tcf(c_81720,plain,
( in(ordered_pair(sK22(sK1,sK1),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_81719,c_987,c_3611]) ).
tcf(c_81779,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = relation_dom(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76825,c_72]) ).
tcf(c_81780,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = relation_rng(sK20(powerset(sK20(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76825,c_71]) ).
tcf(c_81781,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0)))))) = sK20(powerset(sK20(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_76825,c_120]) ).
tcf(c_81800,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_dom(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_78860,c_72]) ).
tcf(c_81801,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_rng(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_78860,c_71]) ).
tcf(c_81802,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = sK20(powerset(relation_rng(sK12))) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_78860,c_120]) ).
tcf(c_81817,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35022]) ).
tcf(c_81818,plain,
( ( sK20(powerset(relation_dom(sK12))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_dom(sK12))))) = sK14(sK1,sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_6419]) ).
tcf(c_81819,plain,
( ( sK20(powerset(relation_dom(sK12))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_dom(sK12))))) = sK5(sK1,sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_5248]) ).
tcf(c_81820,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29434]) ).
tcf(c_81821,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29433]) ).
tcf(c_81822,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29432]) ).
tcf(c_81823,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29048]) ).
tcf(c_81824,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29047]) ).
tcf(c_81825,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29046]) ).
tcf(c_81826,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29001]) ).
tcf(c_81827,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_29000]) ).
tcf(c_81828,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_28999]) ).
tcf(c_81829,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12147]) ).
tcf(c_81830,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3853]) ).
tcf(c_81831,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3852]) ).
tcf(c_81832,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3847]) ).
tcf(c_81833,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3813]) ).
tcf(c_81834,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3812]) ).
tcf(c_81835,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3807]) ).
tcf(c_81836,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_39387]) ).
tcf(c_81837,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_39386]) ).
tcf(c_81838,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_39385]) ).
tcf(c_81839,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34275]) ).
tcf(c_81840,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34274]) ).
tcf(c_81841,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34273]) ).
tcf(c_81842,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34257]) ).
tcf(c_81843,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34256]) ).
tcf(c_81844,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_34255]) ).
tcf(c_81845,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_27401]) ).
tcf(c_81846,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_27400]) ).
tcf(c_81847,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_27399]) ).
tcf(c_81848,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25347]) ).
tcf(c_81849,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25346]) ).
tcf(c_81850,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25345]) ).
tcf(c_81851,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25312]) ).
tcf(c_81852,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25311]) ).
tcf(c_81853,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25310]) ).
tcf(c_81854,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25248]) ).
tcf(c_81855,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25247]) ).
tcf(c_81856,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25246]) ).
tcf(c_81857,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24512]) ).
tcf(c_81858,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24511]) ).
tcf(c_81859,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24510]) ).
tcf(c_81860,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24398]) ).
tcf(c_81861,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24397]) ).
tcf(c_81862,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24396]) ).
tcf(c_81863,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24361]) ).
tcf(c_81864,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24360]) ).
tcf(c_81865,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24359]) ).
tcf(c_81866,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24299]) ).
tcf(c_81867,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24298]) ).
tcf(c_81868,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24297]) ).
tcf(c_81869,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23557]) ).
tcf(c_81870,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23556]) ).
tcf(c_81871,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23555]) ).
tcf(c_81872,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23520]) ).
tcf(c_81873,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23519]) ).
tcf(c_81874,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23518]) ).
tcf(c_81875,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23406]) ).
tcf(c_81876,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23405]) ).
tcf(c_81877,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23404]) ).
tcf(c_81878,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23371]) ).
tcf(c_81879,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23370]) ).
tcf(c_81880,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23369]) ).
tcf(c_81881,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_22305]) ).
tcf(c_81882,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_22304]) ).
tcf(c_81883,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_22303]) ).
tcf(c_81884,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_21079]) ).
tcf(c_81885,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_21078]) ).
tcf(c_81886,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_21077]) ).
tcf(c_81887,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20790]) ).
tcf(c_81888,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20789]) ).
tcf(c_81889,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20788]) ).
tcf(c_81890,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20733]) ).
tcf(c_81891,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20732]) ).
tcf(c_81892,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20731]) ).
tcf(c_81893,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14787]) ).
tcf(c_81894,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20567]) ).
tcf(c_81895,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20566]) ).
tcf(c_81896,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20565]) ).
tcf(c_81897,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19623]) ).
tcf(c_81898,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14242]) ).
tcf(c_81899,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14162]) ).
tcf(c_81900,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14077]) ).
tcf(c_81901,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12144]) ).
tcf(c_81902,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19622]) ).
tcf(c_81903,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19621]) ).
tcf(c_81904,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12143]) ).
tcf(c_81905,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12142]) ).
tcf(c_81906,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12141]) ).
tcf(c_81907,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12140]) ).
tcf(c_81908,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19044]) ).
tcf(c_81909,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19043]) ).
tcf(c_81910,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12139]) ).
tcf(c_81911,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19042]) ).
tcf(c_81912,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18986]) ).
tcf(c_81913,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18985]) ).
tcf(c_81914,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18984]) ).
tcf(c_81915,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_36589]) ).
tcf(c_81916,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18933]) ).
tcf(c_81917,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18932]) ).
tcf(c_81918,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18931]) ).
tcf(c_81919,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18887]) ).
tcf(c_81920,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18886]) ).
tcf(c_81921,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18885]) ).
tcf(c_81922,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18057]) ).
tcf(c_81923,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18056]) ).
tcf(c_81924,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18055]) ).
tcf(c_81925,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17694]) ).
tcf(c_81926,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17693]) ).
tcf(c_81927,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17692]) ).
tcf(c_81928,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17624]) ).
tcf(c_81929,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17623]) ).
tcf(c_81930,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17622]) ).
tcf(c_81931,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17580]) ).
tcf(c_81932,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17579]) ).
tcf(c_81933,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17578]) ).
tcf(c_81934,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17545]) ).
tcf(c_81935,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17544]) ).
tcf(c_81936,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17543]) ).
tcf(c_81937,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_16055]) ).
tcf(c_81938,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_16054]) ).
tcf(c_81939,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_16053]) ).
tcf(c_81940,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15952]) ).
tcf(c_81941,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15951]) ).
tcf(c_81942,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15950]) ).
tcf(c_81943,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15917]) ).
tcf(c_81944,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15916]) ).
tcf(c_81945,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15915]) ).
tcf(c_81946,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15880]) ).
tcf(c_81947,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15879]) ).
tcf(c_81948,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15878]) ).
tcf(c_81949,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12149]) ).
tcf(c_81950,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12148]) ).
tcf(c_81951,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11026]) ).
tcf(c_81952,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11025]) ).
tcf(c_81953,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11024]) ).
tcf(c_81954,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3663]) ).
tcf(c_81955,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3662]) ).
tcf(c_81956,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3661]) ).
tcf(c_81957,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_rng(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3632]) ).
tcf(c_81958,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12146]) ).
tcf(c_81959,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_inverse(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3631]) ).
tcf(c_81960,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_dom(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3626]) ).
tcf(c_81961,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14780]) ).
tcf(c_81962,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14779]) ).
tcf(c_81963,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14778]) ).
tcf(c_81964,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14235]) ).
tcf(c_81965,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14234]) ).
tcf(c_81966,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14233]) ).
tcf(c_81967,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14155]) ).
tcf(c_81968,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14154]) ).
tcf(c_81969,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14153]) ).
tcf(c_81970,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14070]) ).
tcf(c_81971,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14069]) ).
tcf(c_81972,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_14068]) ).
tcf(c_81973,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11811]) ).
tcf(c_81974,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11810]) ).
tcf(c_81975,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11809]) ).
tcf(c_81976,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11771]) ).
tcf(c_81977,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11770]) ).
tcf(c_81978,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11769]) ).
tcf(c_81979,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11729]) ).
tcf(c_81980,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11728]) ).
tcf(c_81981,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11727]) ).
tcf(c_81982,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11691]) ).
tcf(c_81983,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11690]) ).
tcf(c_81984,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11689]) ).
tcf(c_81985,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11660]) ).
tcf(c_81986,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11659]) ).
tcf(c_81987,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11658]) ).
tcf(c_81988,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11297]) ).
tcf(c_81989,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11296]) ).
tcf(c_81990,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_11295]) ).
tcf(c_81991,plain,
( ( sK20(powerset(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_12150]) ).
tcf(c_81992,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_9831]) ).
tcf(c_81993,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_9830]) ).
tcf(c_81994,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_9829]) ).
tcf(c_81995,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3423]) ).
tcf(c_81996,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3422]) ).
tcf(c_81997,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3421]) ).
tcf(c_81998,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3403]) ).
tcf(c_81999,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3402]) ).
tcf(c_82000,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3401]) ).
tcf(c_82001,plain,
( ( function_inverse(sK20(powerset(relation_dom(sK12)))) = relation_inverse(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_957]) ).
tcf(c_82002,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3333]) ).
tcf(c_82003,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK12))) = X0 )
| ~ empty(X0)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_66]) ).
tcf(c_82004,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3330]) ).
tcf(c_82005,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_3327]) ).
tcf(c_82006,plain,
( ( sK20(powerset(relation_dom(sK12))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_133]) ).
tcf(c_82007,plain,
( relation(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_94]) ).
tcf(c_82008,plain,
( function(sK20(powerset(relation_dom(sK12))))
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_85]) ).
tcf(c_82928,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35022]) ).
tcf(c_82929,plain,
( ( sK20(powerset(relation_dom(sK12))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_dom(sK12))))) = sK14(sK1,sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_6419]) ).
tcf(c_82930,plain,
( ( sK20(powerset(relation_dom(sK12))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_dom(sK12))))) = sK5(sK1,sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_5248]) ).
tcf(c_82931,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29434]) ).
tcf(c_82932,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29433]) ).
tcf(c_82933,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29432]) ).
tcf(c_82934,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29048]) ).
tcf(c_82935,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29047]) ).
tcf(c_82936,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29046]) ).
tcf(c_82937,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29001]) ).
tcf(c_82938,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_29000]) ).
tcf(c_82939,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_28999]) ).
tcf(c_82940,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_dom(sK12))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12147]) ).
tcf(c_82941,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3853]) ).
tcf(c_82942,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3852]) ).
tcf(c_82943,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3847]) ).
tcf(c_82944,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3813]) ).
tcf(c_82945,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3812]) ).
tcf(c_82946,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3807]) ).
tcf(c_82947,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_39387]) ).
tcf(c_82948,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_39386]) ).
tcf(c_82949,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_39385]) ).
tcf(c_82950,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34275]) ).
tcf(c_82951,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34274]) ).
tcf(c_82952,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34273]) ).
tcf(c_82953,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34257]) ).
tcf(c_82954,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34256]) ).
tcf(c_82955,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_34255]) ).
tcf(c_82956,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_27401]) ).
tcf(c_82957,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_27400]) ).
tcf(c_82958,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_27399]) ).
tcf(c_82959,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25347]) ).
tcf(c_82960,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25346]) ).
tcf(c_82961,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25345]) ).
tcf(c_82962,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25312]) ).
tcf(c_82963,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25311]) ).
tcf(c_82964,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25310]) ).
tcf(c_82965,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25248]) ).
tcf(c_82966,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25247]) ).
tcf(c_82967,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25246]) ).
tcf(c_82968,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24512]) ).
tcf(c_82969,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24511]) ).
tcf(c_82970,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24510]) ).
tcf(c_82971,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24398]) ).
tcf(c_82972,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24397]) ).
tcf(c_82973,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24396]) ).
tcf(c_82974,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24361]) ).
tcf(c_82975,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24360]) ).
tcf(c_82976,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24359]) ).
tcf(c_82977,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24299]) ).
tcf(c_82978,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24298]) ).
tcf(c_82979,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24297]) ).
tcf(c_82980,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23557]) ).
tcf(c_82981,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23556]) ).
tcf(c_82982,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23555]) ).
tcf(c_82983,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23520]) ).
tcf(c_82984,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23519]) ).
tcf(c_82985,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23518]) ).
tcf(c_82986,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23406]) ).
tcf(c_82987,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23405]) ).
tcf(c_82988,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23404]) ).
tcf(c_82989,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23371]) ).
tcf(c_82990,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23370]) ).
tcf(c_82991,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23369]) ).
tcf(c_82992,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_22305]) ).
tcf(c_82993,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_22304]) ).
tcf(c_82994,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_22303]) ).
tcf(c_82995,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_21079]) ).
tcf(c_82996,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_21078]) ).
tcf(c_82997,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_21077]) ).
tcf(c_82998,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20790]) ).
tcf(c_82999,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20789]) ).
tcf(c_83000,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20788]) ).
tcf(c_83001,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20733]) ).
tcf(c_83002,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20732]) ).
tcf(c_83003,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20731]) ).
tcf(c_83004,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14787]) ).
tcf(c_83005,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20567]) ).
tcf(c_83006,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20566]) ).
tcf(c_83007,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20565]) ).
tcf(c_83008,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19623]) ).
tcf(c_83009,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14242]) ).
tcf(c_83010,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14162]) ).
tcf(c_83011,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14077]) ).
tcf(c_83012,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12144]) ).
tcf(c_83013,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19622]) ).
tcf(c_83014,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19621]) ).
tcf(c_83015,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12143]) ).
tcf(c_83016,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12142]) ).
tcf(c_83017,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12141]) ).
tcf(c_83018,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12140]) ).
tcf(c_83019,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19044]) ).
tcf(c_83020,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19043]) ).
tcf(c_83021,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12139]) ).
tcf(c_83022,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19042]) ).
tcf(c_83023,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18986]) ).
tcf(c_83024,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18985]) ).
tcf(c_83025,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18984]) ).
tcf(c_83026,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_36589]) ).
tcf(c_83027,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18933]) ).
tcf(c_83028,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18932]) ).
tcf(c_83029,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18931]) ).
tcf(c_83030,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18887]) ).
tcf(c_83031,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18886]) ).
tcf(c_83032,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18885]) ).
tcf(c_83033,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18057]) ).
tcf(c_83034,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18056]) ).
tcf(c_83035,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18055]) ).
tcf(c_83036,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17694]) ).
tcf(c_83037,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17693]) ).
tcf(c_83038,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17692]) ).
tcf(c_83039,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17624]) ).
tcf(c_83040,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17623]) ).
tcf(c_83041,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17622]) ).
tcf(c_83042,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17580]) ).
tcf(c_83043,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17579]) ).
tcf(c_83044,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17578]) ).
tcf(c_83045,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17545]) ).
tcf(c_83046,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17544]) ).
tcf(c_83047,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17543]) ).
tcf(c_83048,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_16055]) ).
tcf(c_83049,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_16054]) ).
tcf(c_83050,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_16053]) ).
tcf(c_83051,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15952]) ).
tcf(c_83052,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15951]) ).
tcf(c_83053,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15950]) ).
tcf(c_83054,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15917]) ).
tcf(c_83055,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15916]) ).
tcf(c_83056,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15915]) ).
tcf(c_83057,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15880]) ).
tcf(c_83058,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15879]) ).
tcf(c_83059,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15878]) ).
tcf(c_83060,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12149]) ).
tcf(c_83061,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12148]) ).
tcf(c_83062,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11026]) ).
tcf(c_83063,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11025]) ).
tcf(c_83064,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11024]) ).
tcf(c_83065,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3663]) ).
tcf(c_83066,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3662]) ).
tcf(c_83067,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK12)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3661]) ).
tcf(c_83068,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = relation_rng(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3632]) ).
tcf(c_83069,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12146]) ).
tcf(c_83070,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = relation_inverse(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3631]) ).
tcf(c_83071,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = relation_dom(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3626]) ).
tcf(c_83072,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14780]) ).
tcf(c_83073,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14779]) ).
tcf(c_83074,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14778]) ).
tcf(c_83075,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14235]) ).
tcf(c_83076,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14234]) ).
tcf(c_83077,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14233]) ).
tcf(c_83078,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14155]) ).
tcf(c_83079,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14154]) ).
tcf(c_83080,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14153]) ).
tcf(c_83081,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14070]) ).
tcf(c_83082,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14069]) ).
tcf(c_83083,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_14068]) ).
tcf(c_83084,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11811]) ).
tcf(c_83085,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11810]) ).
tcf(c_83086,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11809]) ).
tcf(c_83087,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11771]) ).
tcf(c_83088,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11770]) ).
tcf(c_83089,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11769]) ).
tcf(c_83090,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11729]) ).
tcf(c_83091,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11728]) ).
tcf(c_83092,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11727]) ).
tcf(c_83093,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11691]) ).
tcf(c_83094,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11690]) ).
tcf(c_83095,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11689]) ).
tcf(c_83096,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11660]) ).
tcf(c_83097,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11659]) ).
tcf(c_83098,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11658]) ).
tcf(c_83099,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11297]) ).
tcf(c_83100,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11296]) ).
tcf(c_83101,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_11295]) ).
tcf(c_83102,plain,
( ( sK20(powerset(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_12150]) ).
tcf(c_83103,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_9831]) ).
tcf(c_83104,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_9830]) ).
tcf(c_83105,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_9829]) ).
tcf(c_83106,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3423]) ).
tcf(c_83107,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3422]) ).
tcf(c_83108,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3421]) ).
tcf(c_83109,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3403]) ).
tcf(c_83110,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3402]) ).
tcf(c_83111,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK12))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3401]) ).
tcf(c_83112,plain,
( ( function_inverse(sK20(powerset(relation_dom(sK12)))) = relation_inverse(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_957]) ).
tcf(c_83113,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3333]) ).
tcf(c_83114,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK12))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_66]) ).
tcf(c_83115,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3330]) ).
tcf(c_83116,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK12)))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_3327]) ).
tcf(c_83117,plain,
( ( sK20(powerset(relation_dom(sK12))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_133]) ).
tcf(c_84003,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35022]) ).
tcf(c_84004,plain,
( ( sK20(powerset(relation_dom(sK9))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(relation_dom(sK9))))) = sK14(sK1,sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_6419]) ).
tcf(c_84005,plain,
( ( sK20(powerset(relation_dom(sK9))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(relation_dom(sK9))))) = sK5(sK1,sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_5248]) ).
tcf(c_84006,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29434]) ).
tcf(c_84007,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29433]) ).
tcf(c_84008,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29432]) ).
tcf(c_84009,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29048]) ).
tcf(c_84010,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29047]) ).
tcf(c_84011,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29046]) ).
tcf(c_84012,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29001]) ).
tcf(c_84013,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_29000]) ).
tcf(c_84014,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_28999]) ).
tcf(c_84015,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(relation_dom(sK9))))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12147]) ).
tcf(c_84016,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3853]) ).
tcf(c_84017,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3852]) ).
tcf(c_84018,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3847]) ).
tcf(c_84019,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3813]) ).
tcf(c_84020,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3812]) ).
tcf(c_84021,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3807]) ).
tcf(c_84022,plain,
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_39387]) ).
tcf(c_84023,plain,
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_39386]) ).
tcf(c_84024,plain,
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_39385]) ).
tcf(c_84025,plain,
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34275]) ).
tcf(c_84026,plain,
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34274]) ).
tcf(c_84027,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34273]) ).
tcf(c_84028,plain,
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34257]) ).
tcf(c_84029,plain,
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34256]) ).
tcf(c_84030,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_34255]) ).
tcf(c_84031,plain,
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_27401]) ).
tcf(c_84032,plain,
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_27400]) ).
tcf(c_84033,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_27399]) ).
tcf(c_84034,plain,
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25347]) ).
tcf(c_84035,plain,
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25346]) ).
tcf(c_84036,plain,
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25345]) ).
tcf(c_84037,plain,
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25312]) ).
tcf(c_84038,plain,
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25311]) ).
tcf(c_84039,plain,
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25310]) ).
tcf(c_84040,plain,
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25248]) ).
tcf(c_84041,plain,
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25247]) ).
tcf(c_84042,plain,
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25246]) ).
tcf(c_84043,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24512]) ).
tcf(c_84044,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24511]) ).
tcf(c_84045,plain,
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24510]) ).
tcf(c_84046,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24398]) ).
tcf(c_84047,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24397]) ).
tcf(c_84048,plain,
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24396]) ).
tcf(c_84049,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24361]) ).
tcf(c_84050,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24360]) ).
tcf(c_84051,plain,
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24359]) ).
tcf(c_84052,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24299]) ).
tcf(c_84053,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24298]) ).
tcf(c_84054,plain,
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24297]) ).
tcf(c_84055,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23557]) ).
tcf(c_84056,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23556]) ).
tcf(c_84057,plain,
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23555]) ).
tcf(c_84058,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23520]) ).
tcf(c_84059,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23519]) ).
tcf(c_84060,plain,
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23518]) ).
tcf(c_84061,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23406]) ).
tcf(c_84062,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23405]) ).
tcf(c_84063,plain,
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23404]) ).
tcf(c_84064,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23371]) ).
tcf(c_84065,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23370]) ).
tcf(c_84066,plain,
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23369]) ).
tcf(c_84067,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_22305]) ).
tcf(c_84068,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_22304]) ).
tcf(c_84069,plain,
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_22303]) ).
tcf(c_84070,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_21079]) ).
tcf(c_84071,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_21078]) ).
tcf(c_84072,plain,
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_21077]) ).
tcf(c_84073,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20790]) ).
tcf(c_84074,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20789]) ).
tcf(c_84075,plain,
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20788]) ).
tcf(c_84076,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20733]) ).
tcf(c_84077,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20732]) ).
tcf(c_84078,plain,
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20731]) ).
tcf(c_84079,plain,
( ( sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14787]) ).
tcf(c_84080,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20567]) ).
tcf(c_84081,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20566]) ).
tcf(c_84082,plain,
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20565]) ).
tcf(c_84083,plain,
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19623]) ).
tcf(c_84084,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14242]) ).
tcf(c_84085,plain,
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14162]) ).
tcf(c_84086,plain,
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14077]) ).
tcf(c_84087,plain,
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12144]) ).
tcf(c_84088,plain,
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19622]) ).
tcf(c_84089,plain,
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19621]) ).
tcf(c_84090,plain,
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12143]) ).
tcf(c_84091,plain,
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12142]) ).
tcf(c_84092,plain,
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12141]) ).
tcf(c_84093,plain,
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12140]) ).
tcf(c_84094,plain,
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19044]) ).
tcf(c_84095,plain,
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19043]) ).
tcf(c_84096,plain,
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12139]) ).
tcf(c_84097,plain,
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19042]) ).
tcf(c_84098,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18986]) ).
tcf(c_84099,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18985]) ).
tcf(c_84100,plain,
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18984]) ).
tcf(c_84101,plain,
( ( sK20(sK19(powerset(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_36589]) ).
tcf(c_84102,plain,
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18933]) ).
tcf(c_84103,plain,
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18932]) ).
tcf(c_84104,plain,
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18931]) ).
tcf(c_84105,plain,
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18887]) ).
tcf(c_84106,plain,
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18886]) ).
tcf(c_84107,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18885]) ).
tcf(c_84108,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18057]) ).
tcf(c_84109,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18056]) ).
tcf(c_84110,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18055]) ).
tcf(c_84111,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17694]) ).
tcf(c_84112,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17693]) ).
tcf(c_84113,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17692]) ).
tcf(c_84114,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17624]) ).
tcf(c_84115,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17623]) ).
tcf(c_84116,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17622]) ).
tcf(c_84117,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17580]) ).
tcf(c_84118,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17579]) ).
tcf(c_84119,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17578]) ).
tcf(c_84120,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17545]) ).
tcf(c_84121,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17544]) ).
tcf(c_84122,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17543]) ).
tcf(c_84123,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_16055]) ).
tcf(c_84124,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_16054]) ).
tcf(c_84125,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_16053]) ).
tcf(c_84126,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15952]) ).
tcf(c_84127,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15951]) ).
tcf(c_84128,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15950]) ).
tcf(c_84129,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15917]) ).
tcf(c_84130,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15916]) ).
tcf(c_84131,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15915]) ).
tcf(c_84132,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15880]) ).
tcf(c_84133,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15879]) ).
tcf(c_84134,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15878]) ).
tcf(c_84135,plain,
( ( relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12149]) ).
tcf(c_84136,plain,
( ( relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12148]) ).
tcf(c_84137,plain,
( ( function_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))) = relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11026]) ).
tcf(c_84138,plain,
( ( function_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))) = relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11025]) ).
tcf(c_84139,plain,
( ( function_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))) = relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11024]) ).
tcf(c_84140,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3663]) ).
tcf(c_84141,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3662]) ).
tcf(c_84142,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK9)))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3661]) ).
tcf(c_84143,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = relation_rng(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3632]) ).
tcf(c_84144,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12146]) ).
tcf(c_84145,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = relation_inverse(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3631]) ).
tcf(c_84146,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = relation_dom(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3626]) ).
tcf(c_84147,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14780]) ).
tcf(c_84148,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14779]) ).
tcf(c_84149,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14778]) ).
tcf(c_84150,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14235]) ).
tcf(c_84151,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14234]) ).
tcf(c_84152,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14233]) ).
tcf(c_84153,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14155]) ).
tcf(c_84154,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14154]) ).
tcf(c_84155,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14153]) ).
tcf(c_84156,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14070]) ).
tcf(c_84157,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14069]) ).
tcf(c_84158,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_14068]) ).
tcf(c_84159,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11811]) ).
tcf(c_84160,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11810]) ).
tcf(c_84161,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11809]) ).
tcf(c_84162,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11771]) ).
tcf(c_84163,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11770]) ).
tcf(c_84164,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11769]) ).
tcf(c_84165,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11729]) ).
tcf(c_84166,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11728]) ).
tcf(c_84167,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11727]) ).
tcf(c_84168,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11691]) ).
tcf(c_84169,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11690]) ).
tcf(c_84170,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11689]) ).
tcf(c_84171,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11660]) ).
tcf(c_84172,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11659]) ).
tcf(c_84173,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11658]) ).
tcf(c_84174,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11297]) ).
tcf(c_84175,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11296]) ).
tcf(c_84176,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_11295]) ).
tcf(c_84177,plain,
( ( sK20(powerset(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_12150]) ).
tcf(c_84178,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_9831]) ).
tcf(c_84179,plain,
( ( relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_9830]) ).
tcf(c_84180,plain,
( ( relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_9829]) ).
tcf(c_84181,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3423]) ).
tcf(c_84182,plain,
( ( relation_rng(relation_rng(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3422]) ).
tcf(c_84183,plain,
( ( relation_rng(relation_dom(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3421]) ).
tcf(c_84184,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3403]) ).
tcf(c_84185,plain,
( ( relation_dom(relation_rng(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3402]) ).
tcf(c_84186,plain,
( ( relation_dom(relation_dom(sK20(powerset(relation_dom(sK9))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3401]) ).
tcf(c_84187,plain,
( ( function_inverse(sK20(powerset(relation_dom(sK9)))) = relation_inverse(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_957]) ).
tcf(c_84188,plain,
( ( relation_inverse(sK20(powerset(relation_dom(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3333]) ).
tcf(c_84189,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK9))) = X0 )
| ~ empty(X0)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_66]) ).
tcf(c_84190,plain,
( ( relation_rng(sK20(powerset(relation_dom(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3330]) ).
tcf(c_84191,plain,
( ( relation_dom(sK20(powerset(relation_dom(sK9)))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_3327]) ).
tcf(c_84192,plain,
( ( sK20(powerset(relation_dom(sK9))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_133]) ).
tcf(c_85108,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_dom(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_75490,c_72]) ).
tcf(c_85109,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_rng(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_75490,c_71]) ).
tcf(c_85110,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = sK20(powerset(relation_dom(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_75490,c_120]) ).
tcf(c_85125,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80973,c_70]) ).
tcf(c_85126,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80973,c_69]) ).
tcf(c_85129,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80973,c_12335]) ).
tcf(c_85130,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80973,c_8396]) ).
tcf(c_85131,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80973,c_8395]) ).
tcf(c_85132,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80973,c_4044]) ).
tcf(c_85133,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80973,c_42224]) ).
tcf(c_85134,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80973,c_12701]) ).
tcf(c_85135,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80973,c_10144]) ).
tcf(c_85136,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80973,c_4468]) ).
tcf(c_85184,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80978,c_70]) ).
tcf(c_85185,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_69]) ).
tcf(c_85188,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_12335]) ).
tcf(c_85189,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_8396]) ).
tcf(c_85190,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_8395]) ).
tcf(c_85191,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_4044]) ).
tcf(c_85192,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80978,c_42224]) ).
tcf(c_85193,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_12701]) ).
tcf(c_85194,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_10144]) ).
tcf(c_85195,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80978,c_4468]) ).
tcf(c_85234,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80982,c_70]) ).
tcf(c_85235,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_69]) ).
tcf(c_85238,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_12335]) ).
tcf(c_85239,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_8396]) ).
tcf(c_85240,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_8395]) ).
tcf(c_85241,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_4044]) ).
tcf(c_85242,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80982,c_42224]) ).
tcf(c_85243,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_12701]) ).
tcf(c_85244,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_10144]) ).
tcf(c_85245,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80982,c_4468]) ).
tcf(c_85284,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ in(relation_dom(sK2),sK24(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_80986,c_70]) ).
tcf(c_85285,plain,
( element(sK24(sK2,sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80986,c_69]) ).
tcf(c_85288,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK2,sK1))) = apply(sK1,sK15(sK1,sK24(sK2,sK1))) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80986,c_12335]) ).
tcf(c_85289,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80986,c_8396]) ).
tcf(c_85290,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK2,sK1)))) = sK15(sK1,sK24(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_80986,c_8395]) ).
tcf(c_85291,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80986,c_4044]) ).
tcf(c_85292,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK24(sK2,sK1)) = apply(sK2,sK24(sK2,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80986,c_42224]) ).
tcf(c_85293,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80986,c_12701]) ).
tcf(c_85294,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK2,sK1))) = sK24(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_80986,c_10144]) ).
tcf(c_85295,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK24(sK2,sK1)) = sK15(sK1,sK24(sK2,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_80986,c_4468]) ).
tcf(c_85337,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_8859]) ).
tcf(c_85339,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_8859]) ).
tcf(c_85340,plain,
( in(sK24(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK2)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_8859]) ).
tcf(c_85341,plain,
( in(sK24(sK1,relation_inverse(sK9)),relation_dom(sK9))
| in(sK23(sK1,relation_inverse(sK9)),relation_dom(sK1))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_8859]) ).
tcf(c_85342,plain,
( in(sK24(sK1,relation_inverse(sK10)),relation_dom(sK10))
| in(sK23(sK1,relation_inverse(sK10)),relation_dom(sK1))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_8859]) ).
tcf(c_85344,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK24(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8859,c_70]) ).
tcf(c_85345,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| element(sK24(sK1,X0),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8859,c_69]) ).
tcf(c_85346,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8859,c_67]) ).
tcf(c_85347,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK1,sK2))) = sK24(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8859,c_43161]) ).
tcf(c_85348,plain,
( in(sK23(sK1,sK9),relation_dom(sK1))
| ( sK1 = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8859,c_29938]) ).
tcf(c_85349,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8859,c_69454]) ).
tcf(c_85351,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85349,c_95]) ).
tcf(c_85355,plain,
( in(sK23(sK1,sK9),relation_dom(sK1))
| ( sK1 = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85348,c_83]) ).
tcf(c_85383,plain,
( in(sK24(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85339,c_3610]) ).
tcf(c_85387,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85337,c_3611]) ).
tcf(c_85458,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4030,c_8860]) ).
tcf(c_85460,plain,
( in(sK23(sK1,relation_inverse(sK2)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK2)),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_8860]) ).
tcf(c_85461,plain,
( in(sK23(sK1,relation_inverse(sK9)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK9)),relation_rng(sK9))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_8860]) ).
tcf(c_85462,plain,
( in(sK23(sK1,relation_inverse(sK10)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK10)),relation_rng(sK10))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_8860]) ).
tcf(c_85463,plain,
( in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_8860]) ).
tcf(c_85464,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK1),sK23(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8860,c_70]) ).
tcf(c_85465,plain,
! [X0: $i] :
( element(sK23(sK1,X0),relation_dom(sK1))
| in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_69]) ).
tcf(c_85468,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0)))) = apply(sK1,sK23(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_12766]) ).
tcf(c_85469,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0)))) = sK7(sK1,sK23(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_12765]) ).
tcf(c_85470,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,X0)))) = apply(sK1,sK23(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_10203]) ).
tcf(c_85471,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0)))) = sK7(sK1,sK23(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_10202]) ).
tcf(c_85472,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0))) = sK15(sK1,apply(sK1,sK23(sK1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_6249]) ).
tcf(c_85473,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0))) = sK15(sK1,sK7(sK1,sK23(sK1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_5349]) ).
tcf(c_85475,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK23(sK1,X0)) = apply(sK1,sK23(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_12284]) ).
tcf(c_85476,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_4619]) ).
tcf(c_85477,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_4406]) ).
tcf(c_85478,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK23(sK1,X0)) ),
inference(superposition,[status(thm)],[c_8860,c_70]) ).
tcf(c_85479,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| element(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_69]) ).
tcf(c_85480,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8860,c_67]) ).
tcf(c_85492,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_12335]) ).
tcf(c_85493,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_8396]) ).
tcf(c_85494,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_8395]) ).
tcf(c_85495,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_4044]) ).
tcf(c_85496,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK1,sK2)) = apply(sK2,sK23(sK1,sK2)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8860,c_42224]) ).
tcf(c_85497,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_12701]) ).
tcf(c_85498,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_10144]) ).
tcf(c_85499,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8860,c_4468]) ).
tcf(c_85500,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8860,c_68472]) ).
tcf(c_85505,plain,
( in(sK23(sK1,sK12),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85500,c_95]) ).
tcf(c_85529,plain,
( in(sK23(sK1,relation_inverse(sK12)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85463,c_3610]) ).
tcf(c_85545,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85458,c_3611]) ).
tcf(c_85549,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85499,c_61]) ).
tcf(c_85553,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85498,c_61]) ).
tcf(c_85557,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85497,c_61]) ).
tcf(c_85574,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85495,c_61]) ).
tcf(c_85579,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85494,c_61]) ).
tcf(c_85583,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85493,c_61]) ).
tcf(c_85587,plain,
( in(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85492,c_61]) ).
tcf(c_85814,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85549,c_70]) ).
tcf(c_85815,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_69]) ).
tcf(c_85818,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_12766]) ).
tcf(c_85819,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_12765]) ).
tcf(c_85820,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_10203]) ).
tcf(c_85821,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_10202]) ).
tcf(c_85822,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85549,c_6249]) ).
tcf(c_85823,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85549,c_5349]) ).
tcf(c_85825,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85549,c_12284]) ).
tcf(c_85826,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85549,c_4619]) ).
tcf(c_85827,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85549,c_4406]) ).
tcf(c_85871,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85553,c_70]) ).
tcf(c_85872,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85553,c_69]) ).
tcf(c_85875,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85553,c_12766]) ).
tcf(c_85876,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85553,c_12765]) ).
tcf(c_85877,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85553,c_10203]) ).
tcf(c_85878,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85553,c_10202]) ).
tcf(c_85879,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85553,c_6249]) ).
tcf(c_85880,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85553,c_5349]) ).
tcf(c_85882,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85553,c_12284]) ).
tcf(c_85883,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85553,c_4619]) ).
tcf(c_85884,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85553,c_4406]) ).
tcf(c_85934,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_18305,c_87]) ).
tcf(c_85935,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18305,c_13473]) ).
tcf(c_85936,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18305,c_13472]) ).
tcf(c_85937,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_18305,c_34564]) ).
tcf(c_85938,plain,
( element(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18305,c_34565]) ).
tcf(c_85939,plain,
( in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18305,c_34571]) ).
tcf(c_85940,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18305,c_34529]) ).
tcf(c_85941,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18305,c_12764]) ).
tcf(c_85942,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18305,c_13488]) ).
tcf(c_85943,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18305,c_12807]) ).
tcf(c_85944,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18305,c_4623]) ).
tcf(c_85945,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18305,c_17971]) ).
tcf(c_85946,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18305,c_50582]) ).
tcf(c_85947,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18305,c_12789]) ).
tcf(c_86010,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_85934,c_4030]) ).
tcf(c_86011,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86010,c_987,c_3611]) ).
tcf(c_86285,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_dom(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_82007,c_72]) ).
tcf(c_86286,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12))))) = relation_rng(sK20(powerset(relation_dom(sK12)))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_82007,c_71]) ).
tcf(c_86287,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12))))) = sK20(powerset(relation_dom(sK12))) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_82007,c_120]) ).
tcf(c_86302,plain,
( ( sK20(powerset(relation_rng(sK9))) = empty_set )
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_77711]) ).
tcf(c_86312,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9))))) = relation_dom(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_75492,c_72]) ).
tcf(c_86313,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9))))) = relation_rng(sK20(powerset(relation_dom(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_75492,c_71]) ).
tcf(c_86314,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9))))) = sK20(powerset(relation_dom(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_75492,c_120]) ).
tcf(c_86336,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9))))) = relation_dom(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_76570,c_72]) ).
tcf(c_86337,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9))))) = relation_rng(sK20(powerset(relation_rng(sK9)))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_76570,c_71]) ).
tcf(c_86338,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9))))) = sK20(powerset(relation_rng(sK9))) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_76570,c_120]) ).
tcf(c_86351,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85557,c_70]) ).
tcf(c_86352,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85557,c_69]) ).
tcf(c_86355,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85557,c_12766]) ).
tcf(c_86356,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85557,c_12765]) ).
tcf(c_86357,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85557,c_10203]) ).
tcf(c_86358,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85557,c_10202]) ).
tcf(c_86359,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85557,c_6249]) ).
tcf(c_86360,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85557,c_5349]) ).
tcf(c_86362,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85557,c_12284]) ).
tcf(c_86363,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85557,c_4619]) ).
tcf(c_86364,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85557,c_4406]) ).
tcf(c_86542,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85574,c_70]) ).
tcf(c_86543,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85574,c_69]) ).
tcf(c_86546,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85574,c_12766]) ).
tcf(c_86547,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85574,c_12765]) ).
tcf(c_86548,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85574,c_10203]) ).
tcf(c_86549,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85574,c_10202]) ).
tcf(c_86550,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85574,c_6249]) ).
tcf(c_86551,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85574,c_5349]) ).
tcf(c_86553,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85574,c_12284]) ).
tcf(c_86554,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85574,c_4619]) ).
tcf(c_86555,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85574,c_4406]) ).
tcf(c_86610,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85579,c_70]) ).
tcf(c_86611,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_69]) ).
tcf(c_86614,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_12766]) ).
tcf(c_86615,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_12765]) ).
tcf(c_86616,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_10203]) ).
tcf(c_86617,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_10202]) ).
tcf(c_86618,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_6249]) ).
tcf(c_86619,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_5349]) ).
tcf(c_86621,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_12284]) ).
tcf(c_86622,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_4619]) ).
tcf(c_86623,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_4406]) ).
tcf(c_86667,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85583,c_70]) ).
tcf(c_86668,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_69]) ).
tcf(c_86671,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_12766]) ).
tcf(c_86672,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_12765]) ).
tcf(c_86673,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_10203]) ).
tcf(c_86674,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_10202]) ).
tcf(c_86675,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_6249]) ).
tcf(c_86676,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_5349]) ).
tcf(c_86678,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_12284]) ).
tcf(c_86679,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_4619]) ).
tcf(c_86680,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_4406]) ).
tcf(c_86724,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ~ in(relation_dom(sK1),sK23(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_85587,c_70]) ).
tcf(c_86725,plain,
( element(sK23(sK1,sK2),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85587,c_69]) ).
tcf(c_86728,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85587,c_12766]) ).
tcf(c_86729,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85587,c_12765]) ).
tcf(c_86730,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2)))) = apply(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85587,c_10203]) ).
tcf(c_86731,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2)))) = sK7(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85587,c_10202]) ).
tcf(c_86732,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK15(sK1,apply(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85587,c_6249]) ).
tcf(c_86733,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK15(sK1,sK7(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85587,c_5349]) ).
tcf(c_86735,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK1,sK2)) = apply(sK1,sK23(sK1,sK2)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85587,c_12284]) ).
tcf(c_86736,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85587,c_4619]) ).
tcf(c_86737,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85587,c_4406]) ).
tcf(c_86784,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_3821,c_8978]) ).
tcf(c_86786,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_8978]) ).
tcf(c_86787,plain,
( in(sK24(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_8978]) ).
tcf(c_86788,plain,
( in(sK24(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK23(relation_inverse(sK9),sK1),relation_dom(sK1))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_8978]) ).
tcf(c_86789,plain,
( in(sK24(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK23(relation_inverse(sK10),sK1),relation_dom(sK1))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_8978]) ).
tcf(c_86791,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK24(X0,sK1)) ),
inference(superposition,[status(thm)],[c_8978,c_70]) ).
tcf(c_86792,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| element(sK24(X0,sK1),relation_rng(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8978,c_69]) ).
tcf(c_86793,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8978,c_67]) ).
tcf(c_86794,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK24(sK2,sK1))) = sK24(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8978,c_43161]) ).
tcf(c_86795,plain,
( in(sK23(sK9,sK1),relation_dom(sK1))
| ( sK1 = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_8978,c_29938]) ).
tcf(c_86796,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_8978,c_69454]) ).
tcf(c_86798,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86796,c_95]) ).
tcf(c_86802,plain,
( in(sK23(sK9,sK1),relation_dom(sK1))
| ( sK1 = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86795,c_83]) ).
tcf(c_86830,plain,
( in(sK24(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86786,c_3610]) ).
tcf(c_86834,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86784,c_3611]) ).
tcf(c_86847,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_4030,c_8979]) ).
tcf(c_86849,plain,
( in(sK23(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_8979]) ).
tcf(c_86850,plain,
( in(sK23(relation_inverse(sK9),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_8979]) ).
tcf(c_86851,plain,
( in(sK23(relation_inverse(sK10),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( relation_inverse(sK10) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_8979]) ).
tcf(c_86852,plain,
( in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_8979]) ).
tcf(c_86853,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK1),sK23(X0,sK1)) ),
inference(superposition,[status(thm)],[c_8979,c_70]) ).
tcf(c_86854,plain,
! [X0: $i] :
( element(sK23(X0,sK1),relation_dom(sK1))
| in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_69]) ).
tcf(c_86857,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1)))) = apply(sK1,sK23(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_12766]) ).
tcf(c_86858,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1)))) = sK7(sK1,sK23(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_12765]) ).
tcf(c_86859,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(X0,sK1)))) = apply(sK1,sK23(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_10203]) ).
tcf(c_86860,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1)))) = sK7(sK1,sK23(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_10202]) ).
tcf(c_86861,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1))) = sK15(sK1,apply(sK1,sK23(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_6249]) ).
tcf(c_86862,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1))) = sK15(sK1,sK7(sK1,sK23(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_5349]) ).
tcf(c_86864,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( sK15(relation_inverse(sK1),sK23(X0,sK1)) = apply(sK1,sK23(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_12284]) ).
tcf(c_86865,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_4619]) ).
tcf(c_86866,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_4406]) ).
tcf(c_86867,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK23(X0,sK1)) ),
inference(superposition,[status(thm)],[c_8979,c_70]) ).
tcf(c_86868,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| element(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_69]) ).
tcf(c_86869,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(sK1))
| ( X0 = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_8979,c_67]) ).
tcf(c_86881,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_12335]) ).
tcf(c_86882,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_8396]) ).
tcf(c_86883,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_8395]) ).
tcf(c_86884,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_4044]) ).
tcf(c_86885,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK2),sK23(sK2,sK1)) = apply(sK2,sK23(sK2,sK1)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_8979,c_42224]) ).
tcf(c_86886,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_12701]) ).
tcf(c_86887,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_10144]) ).
tcf(c_86888,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_8979,c_4468]) ).
tcf(c_86889,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_8979,c_68472]) ).
tcf(c_86894,plain,
( in(sK23(sK12,sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86889,c_95]) ).
tcf(c_86918,plain,
( in(sK23(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(sK12) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86852,c_3610]) ).
tcf(c_86934,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86847,c_3611]) ).
tcf(c_86938,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86888,c_61]) ).
tcf(c_86942,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86887,c_61]) ).
tcf(c_86946,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86886,c_61]) ).
tcf(c_86963,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86884,c_61]) ).
tcf(c_86968,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86883,c_61]) ).
tcf(c_86972,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86882,c_61]) ).
tcf(c_86976,plain,
( in(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86881,c_61]) ).
tcf(c_87015,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86938,c_70]) ).
tcf(c_87016,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_69]) ).
tcf(c_87019,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_12766]) ).
tcf(c_87020,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_12765]) ).
tcf(c_87021,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_10203]) ).
tcf(c_87022,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_10202]) ).
tcf(c_87023,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86938,c_6249]) ).
tcf(c_87024,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86938,c_5349]) ).
tcf(c_87026,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86938,c_12284]) ).
tcf(c_87027,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86938,c_4619]) ).
tcf(c_87028,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86938,c_4406]) ).
tcf(c_87134,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_18307,c_87]) ).
tcf(c_87135,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18307,c_13473]) ).
tcf(c_87136,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18307,c_13472]) ).
tcf(c_87137,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_18307,c_34564]) ).
tcf(c_87138,plain,
( element(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18307,c_34565]) ).
tcf(c_87139,plain,
( in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18307,c_34571]) ).
tcf(c_87140,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18307,c_34529]) ).
tcf(c_87141,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18307,c_12764]) ).
tcf(c_87142,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18307,c_13488]) ).
tcf(c_87143,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18307,c_12807]) ).
tcf(c_87144,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18307,c_4623]) ).
tcf(c_87145,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( sK15(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_18307,c_17971]) ).
tcf(c_87146,plain,
( in(ordered_pair(sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18307,c_50582]) ).
tcf(c_87147,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK15(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_18307,c_12789]) ).
tcf(c_87209,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_87134,c_4030]) ).
tcf(c_87210,plain,
( in(ordered_pair(sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_87209,c_987,c_3611]) ).
tcf(c_87316,plain,
( ( sK20(powerset(relation_rng(sK12))) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_73,c_78859]) ).
tcf(c_87328,plain,
( ( sK20(powerset(relation_dom(sK12))) = empty_set )
| ~ empty(sK12) ),
inference(superposition,[status(thm)],[c_101,c_82006]) ).
tcf(c_87338,plain,
( ( relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_dom(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_76572,c_72]) ).
tcf(c_87339,plain,
( ( relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12))))) = relation_rng(sK20(powerset(relation_rng(sK12)))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_76572,c_71]) ).
tcf(c_87340,plain,
( ( relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12))))) = sK20(powerset(relation_rng(sK12))) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_76572,c_120]) ).
tcf(c_87360,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35022]) ).
tcf(c_87361,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(powerset(X0))))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(sK20(sK19(powerset(X0))))))) = sK14(sK1,sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_6419]) ).
tcf(c_87362,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(powerset(X0))))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(sK20(sK19(powerset(X0))))))) = sK5(sK1,sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_5248]) ).
tcf(c_87363,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29434]) ).
tcf(c_87364,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29433]) ).
tcf(c_87365,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29432]) ).
tcf(c_87366,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29048]) ).
tcf(c_87367,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29047]) ).
tcf(c_87368,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29046]) ).
tcf(c_87369,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29001]) ).
tcf(c_87370,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_29000]) ).
tcf(c_87371,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_28999]) ).
tcf(c_87372,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12147]) ).
tcf(c_87373,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3853]) ).
tcf(c_87374,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3852]) ).
tcf(c_87375,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3847]) ).
tcf(c_87376,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3813]) ).
tcf(c_87377,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3812]) ).
tcf(c_87378,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3807]) ).
tcf(c_87379,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_39387]) ).
tcf(c_87380,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_39386]) ).
tcf(c_87381,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_39385]) ).
tcf(c_87382,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34275]) ).
tcf(c_87383,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34274]) ).
tcf(c_87384,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34273]) ).
tcf(c_87385,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34257]) ).
tcf(c_87386,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34256]) ).
tcf(c_87387,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_34255]) ).
tcf(c_87388,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_27401]) ).
tcf(c_87389,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_27400]) ).
tcf(c_87390,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_27399]) ).
tcf(c_87391,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25347]) ).
tcf(c_87392,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25346]) ).
tcf(c_87393,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25345]) ).
tcf(c_87394,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25312]) ).
tcf(c_87395,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25311]) ).
tcf(c_87396,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25310]) ).
tcf(c_87397,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25248]) ).
tcf(c_87398,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25247]) ).
tcf(c_87399,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25246]) ).
tcf(c_87400,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24512]) ).
tcf(c_87401,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24511]) ).
tcf(c_87402,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24510]) ).
tcf(c_87403,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24398]) ).
tcf(c_87404,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24397]) ).
tcf(c_87405,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24396]) ).
tcf(c_87406,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24361]) ).
tcf(c_87407,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24360]) ).
tcf(c_87408,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24359]) ).
tcf(c_87409,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24299]) ).
tcf(c_87410,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24298]) ).
tcf(c_87411,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24297]) ).
tcf(c_87412,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23557]) ).
tcf(c_87413,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23556]) ).
tcf(c_87414,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23555]) ).
tcf(c_87415,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23520]) ).
tcf(c_87416,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23519]) ).
tcf(c_87417,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23518]) ).
tcf(c_87418,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23406]) ).
tcf(c_87419,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23405]) ).
tcf(c_87420,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23404]) ).
tcf(c_87421,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23371]) ).
tcf(c_87422,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23370]) ).
tcf(c_87423,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23369]) ).
tcf(c_87424,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_22305]) ).
tcf(c_87425,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_22304]) ).
tcf(c_87426,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_22303]) ).
tcf(c_87427,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_21079]) ).
tcf(c_87428,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_21078]) ).
tcf(c_87429,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_21077]) ).
tcf(c_87430,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20790]) ).
tcf(c_87431,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20789]) ).
tcf(c_87432,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20788]) ).
tcf(c_87433,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20733]) ).
tcf(c_87434,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20732]) ).
tcf(c_87435,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20731]) ).
tcf(c_87436,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14787]) ).
tcf(c_87437,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20567]) ).
tcf(c_87438,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20566]) ).
tcf(c_87439,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20565]) ).
tcf(c_87440,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19623]) ).
tcf(c_87441,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14242]) ).
tcf(c_87442,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14162]) ).
tcf(c_87443,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14077]) ).
tcf(c_87444,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12144]) ).
tcf(c_87445,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19622]) ).
tcf(c_87446,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19621]) ).
tcf(c_87447,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12143]) ).
tcf(c_87448,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12142]) ).
tcf(c_87449,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12141]) ).
tcf(c_87450,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12140]) ).
tcf(c_87451,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19044]) ).
tcf(c_87452,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19043]) ).
tcf(c_87453,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12139]) ).
tcf(c_87454,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19042]) ).
tcf(c_87455,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18986]) ).
tcf(c_87456,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18985]) ).
tcf(c_87457,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18984]) ).
tcf(c_87458,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_36589]) ).
tcf(c_87459,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18933]) ).
tcf(c_87460,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18932]) ).
tcf(c_87461,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18931]) ).
tcf(c_87462,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18887]) ).
tcf(c_87463,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18886]) ).
tcf(c_87464,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18885]) ).
tcf(c_87465,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18057]) ).
tcf(c_87466,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18056]) ).
tcf(c_87467,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18055]) ).
tcf(c_87468,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17694]) ).
tcf(c_87469,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17693]) ).
tcf(c_87470,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17692]) ).
tcf(c_87471,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17624]) ).
tcf(c_87472,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17623]) ).
tcf(c_87473,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17622]) ).
tcf(c_87474,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17580]) ).
tcf(c_87475,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17579]) ).
tcf(c_87476,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17578]) ).
tcf(c_87477,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17545]) ).
tcf(c_87478,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17544]) ).
tcf(c_87479,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17543]) ).
tcf(c_87480,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_16055]) ).
tcf(c_87481,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_16054]) ).
tcf(c_87482,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_16053]) ).
tcf(c_87483,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15952]) ).
tcf(c_87484,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15951]) ).
tcf(c_87485,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15950]) ).
tcf(c_87486,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15917]) ).
tcf(c_87487,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15916]) ).
tcf(c_87488,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15915]) ).
tcf(c_87489,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15880]) ).
tcf(c_87490,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15879]) ).
tcf(c_87491,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15878]) ).
tcf(c_87492,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12149]) ).
tcf(c_87493,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12148]) ).
tcf(c_87494,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11026]) ).
tcf(c_87495,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) = relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11025]) ).
tcf(c_87496,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) = relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11024]) ).
tcf(c_87497,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3663]) ).
tcf(c_87498,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3662]) ).
tcf(c_87499,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3661]) ).
tcf(c_87500,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3632]) ).
tcf(c_87501,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_12146]) ).
tcf(c_87502,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3631]) ).
tcf(c_87503,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_3626]) ).
tcf(c_87504,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14780]) ).
tcf(c_87505,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14779]) ).
tcf(c_87506,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14778]) ).
tcf(c_87507,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14235]) ).
tcf(c_87508,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14234]) ).
tcf(c_87509,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14233]) ).
tcf(c_87510,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14155]) ).
tcf(c_87511,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14154]) ).
tcf(c_87512,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14153]) ).
tcf(c_87513,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14070]) ).
tcf(c_87514,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14069]) ).
tcf(c_87515,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_14068]) ).
tcf(c_87516,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11811]) ).
tcf(c_87517,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11810]) ).
tcf(c_87518,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11809]) ).
tcf(c_87519,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11771]) ).
tcf(c_87520,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11770]) ).
tcf(c_87521,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11769]) ).
tcf(c_87522,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11729]) ).
tcf(c_87523,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11728]) ).
tcf(c_87524,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11727]) ).
tcf(c_87525,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11691]) ).
tcf(c_87526,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11690]) ).
tcf(c_87527,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11689]) ).
tcf(c_87528,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11660]) ).
tcf(c_87529,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11659]) ).
tcf(c_87530,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11658]) ).
tcf(c_87531,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11297]) ).
tcf(c_87532,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11296]) ).
tcf(c_87533,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_11295]) ).
tcf(c_87544,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))) = relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_957]) ).
tcf(c_87550,plain,
! [X0: $i] :
( relation(sK20(powerset(sK20(sK19(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_94]) ).
tcf(c_87551,plain,
! [X0: $i] :
( function(sK20(powerset(sK20(sK19(powerset(X0))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_85]) ).
tcf(c_88525,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86942,c_70]) ).
tcf(c_88526,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86942,c_69]) ).
tcf(c_88529,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86942,c_12766]) ).
tcf(c_88530,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86942,c_12765]) ).
tcf(c_88531,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86942,c_10203]) ).
tcf(c_88532,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86942,c_10202]) ).
tcf(c_88533,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86942,c_6249]) ).
tcf(c_88534,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86942,c_5349]) ).
tcf(c_88536,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86942,c_12284]) ).
tcf(c_88537,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86942,c_4619]) ).
tcf(c_88538,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86942,c_4406]) ).
tcf(c_88582,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86946,c_70]) ).
tcf(c_88583,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86946,c_69]) ).
tcf(c_88586,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86946,c_12766]) ).
tcf(c_88587,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86946,c_12765]) ).
tcf(c_88588,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86946,c_10203]) ).
tcf(c_88589,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86946,c_10202]) ).
tcf(c_88590,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86946,c_6249]) ).
tcf(c_88591,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86946,c_5349]) ).
tcf(c_88593,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86946,c_12284]) ).
tcf(c_88594,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86946,c_4619]) ).
tcf(c_88595,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86946,c_4406]) ).
tcf(c_88860,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86963,c_70]) ).
tcf(c_88861,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86963,c_69]) ).
tcf(c_88864,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86963,c_12766]) ).
tcf(c_88865,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86963,c_12765]) ).
tcf(c_88866,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86963,c_10203]) ).
tcf(c_88867,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86963,c_10202]) ).
tcf(c_88868,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86963,c_6249]) ).
tcf(c_88869,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86963,c_5349]) ).
tcf(c_88871,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86963,c_12284]) ).
tcf(c_88872,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86963,c_4619]) ).
tcf(c_88873,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86963,c_4406]) ).
tcf(c_88928,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86968,c_70]) ).
tcf(c_88929,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_69]) ).
tcf(c_88932,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_12766]) ).
tcf(c_88933,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_12765]) ).
tcf(c_88934,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_10203]) ).
tcf(c_88935,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_10202]) ).
tcf(c_88936,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_6249]) ).
tcf(c_88937,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_5349]) ).
tcf(c_88939,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_12284]) ).
tcf(c_88940,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_4619]) ).
tcf(c_88941,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_4406]) ).
tcf(c_88985,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86972,c_70]) ).
tcf(c_88986,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_69]) ).
tcf(c_88989,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_12766]) ).
tcf(c_88990,plain,
( ( sK1 = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_12765]) ).
tcf(c_88991,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_10203]) ).
tcf(c_88992,plain,
( ( sK1 = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_10202]) ).
tcf(c_88993,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_6249]) ).
tcf(c_88994,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_5349]) ).
tcf(c_88996,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_12284]) ).
tcf(c_88997,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_4619]) ).
tcf(c_88998,plain,
( ( sK1 = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_4406]) ).
tcf(c_89042,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ~ in(relation_dom(sK1),sK23(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_86976,c_70]) ).
tcf(c_89043,plain,
( element(sK23(sK2,sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86976,c_69]) ).
tcf(c_89046,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86976,c_12766]) ).
tcf(c_89047,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86976,c_12765]) ).
tcf(c_89048,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1)))) = apply(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86976,c_10203]) ).
tcf(c_89049,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1)))) = sK7(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86976,c_10202]) ).
tcf(c_89050,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK15(sK1,apply(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86976,c_6249]) ).
tcf(c_89051,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK15(sK1,sK7(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86976,c_5349]) ).
tcf(c_89053,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK23(sK2,sK1)) = apply(sK1,sK23(sK2,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86976,c_12284]) ).
tcf(c_89054,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86976,c_4619]) ).
tcf(c_89055,plain,
( ( sK1 = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86976,c_4406]) ).
tcf(c_89099,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_89,c_10491]) ).
tcf(c_89100,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_57900,c_10491]) ).
tcf(c_89101,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,sK7(sK1,sK7(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_56474,c_10491]) ).
tcf(c_89104,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89099,c_65,c_64]) ).
tcf(c_89123,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_89104]) ).
tcf(c_89124,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_89104]) ).
tcf(c_89125,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_89104]) ).
tcf(c_89126,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_89104]) ).
tcf(c_89128,plain,
( ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_89104]) ).
tcf(c_89130,plain,
( ( apply(sK2,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_89104]) ).
tcf(c_89214,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_87550,c_72]) ).
tcf(c_89215,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_87550,c_71]) ).
tcf(c_89216,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0))))))) = sK20(powerset(sK20(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_87550,c_120]) ).
tcf(c_89249,plain,
! [X0: $i] :
( empty(X0)
| element(sK20(sK19(sK19(X0))),X0) ),
inference(global_subsumption_just,[status(thm)],[c_36526,c_118,c_36526]) ).
tcf(c_89256,plain,
! [X0: $i] :
( empty(X0)
| in(sK20(sK19(sK19(X0))),X0) ),
inference(superposition,[status(thm)],[c_89249,c_68]) ).
tcf(c_89257,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| element(X0,X1)
| ~ in(X0,sK20(sK19(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_89249,c_114]) ).
tcf(c_89258,plain,
! [X0: $i,X1: $i] :
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(X0,sK20(sK19(sK19(powerset(X1))))) ),
inference(superposition,[status(thm)],[c_89249,c_113]) ).
tcf(c_89261,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,sK20(sK19(sK19(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89258,c_137]) ).
tcf(c_89264,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,sK20(sK19(sK19(powerset(X1))))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89257,c_137]) ).
tcf(c_89274,plain,
! [X0: $i] :
( empty(X0)
| ~ in(X0,sK20(sK19(sK19(X0)))) ),
inference(superposition,[status(thm)],[c_89256,c_70]) ).
tcf(c_89278,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_12766]) ).
tcf(c_89279,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_12765]) ).
tcf(c_89280,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_10203]) ).
tcf(c_89281,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_10202]) ).
tcf(c_89282,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK15(sK1,apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_6249]) ).
tcf(c_89283,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK15(sK1,sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_5349]) ).
tcf(c_89285,plain,
( empty(relation_dom(sK1))
| ( sK15(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK1))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_12284]) ).
tcf(c_89286,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_4619]) ).
tcf(c_89287,plain,
( empty(relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_4406]) ).
tcf(c_89289,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(sK19(sK19(relation_dom(sK2)))))) = apply(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2)))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_12335]) ).
tcf(c_89290,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_8396]) ).
tcf(c_89291,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_8395]) ).
tcf(c_89292,plain,
( empty(relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_4044]) ).
tcf(c_89293,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK2),sK20(sK19(sK19(relation_dom(sK2))))) = apply(sK2,sK20(sK19(sK19(relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_89256,c_42224]) ).
tcf(c_89294,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,apply(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_12701]) ).
tcf(c_89295,plain,
( empty(relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_10144]) ).
tcf(c_89296,plain,
( empty(relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))) ) ),
inference(superposition,[status(thm)],[c_89256,c_4468]) ).
tcf(c_89297,plain,
! [X0: $i] :
( empty(X0)
| empty(sK19(X0))
| element(sK20(sK19(sK19(sK19(X0)))),X0) ),
inference(superposition,[status(thm)],[c_89256,c_4215]) ).
tcf(c_89298,plain,
! [X0: $i] :
( empty(sK20(powerset(X0)))
| element(sK20(sK19(sK19(sK20(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_89256,c_4216]) ).
tcf(c_89300,plain,
( empty(relation_rng(sK2))
| ( apply(sK2,sK7(relation_inverse(sK2),sK20(sK19(sK19(relation_rng(sK2)))))) = sK20(sK19(sK19(relation_rng(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_89256,c_43161]) ).
tcf(c_89307,plain,
! [X0: $i] :
( empty(sK20(sK19(powerset(X0))))
| element(sK20(sK19(sK19(sK20(sK19(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_89256,c_36119]) ).
tcf(c_89488,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),sK14(sK1,X0)) ),
inference(superposition,[status(thm)],[c_10592,c_70]) ).
tcf(c_89492,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10592,c_12766]) ).
tcf(c_89493,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10592,c_12765]) ).
tcf(c_89494,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK14(sK1,X0)))) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10592,c_10203]) ).
tcf(c_89495,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0)))) = sK7(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10592,c_10202]) ).
tcf(c_89496,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK15(sK1,apply(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_10592,c_6249]) ).
tcf(c_89497,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK15(sK1,sK7(sK1,sK14(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_10592,c_5349]) ).
tcf(c_89499,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK1),sK14(sK1,X0)) = apply(sK1,sK14(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10592,c_12284]) ).
tcf(c_89500,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10592,c_4619]) ).
tcf(c_89501,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10592,c_4406]) ).
tcf(c_89590,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),sK13(sK1,X0)) ),
inference(superposition,[status(thm)],[c_10594,c_70]) ).
tcf(c_89594,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK13(sK1,X0))) = apply(sK1,sK15(sK1,sK13(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_10594,c_12335]) ).
tcf(c_89595,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10594,c_8396]) ).
tcf(c_89596,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK13(sK1,X0)))) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10594,c_8395]) ).
tcf(c_89597,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,apply(sK2,sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10594,c_4044]) ).
tcf(c_89598,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK2),sK13(sK1,X0)) = apply(sK2,sK13(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_10594,c_42224]) ).
tcf(c_89599,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10594,c_12701]) ).
tcf(c_89600,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10594,c_10144]) ).
tcf(c_89601,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK15(sK1,sK13(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_10594,c_4468]) ).
tcf(c_89682,plain,
( ( sK20(powerset(relation_dom(sK9))) = empty_set )
| ~ empty(sK9) ),
inference(superposition,[status(thm)],[c_121,c_84192]) ).
tcf(c_89777,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(sK19(sK19(powerset(X0)))),X1),X1)
| ( relation_dom(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_77,c_89261]) ).
tcf(c_89778,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_dom(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_79,c_89261]) ).
tcf(c_89779,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ function(sK20(sK19(sK19(powerset(X1)))))
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_dom(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_87,c_89261]) ).
tcf(c_89780,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(sK19(sK19(powerset(X0)))),X1),X1)
| ( relation_rng(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_105,c_89261]) ).
tcf(c_89781,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_rng(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_107,c_89261]) ).
tcf(c_89782,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK21(sK20(sK19(sK19(powerset(X0)))),X1),sK22(sK20(sK19(sK19(powerset(X0)))),X1)),X1)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_125,c_89261]) ).
tcf(c_89783,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK22(X1,sK20(sK19(sK19(powerset(X0))))),sK21(X1,sK20(sK19(sK19(powerset(X0)))))),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(X1) )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_125,c_89261]) ).
tcf(c_89784,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(X1,sK20(sK19(sK19(powerset(X0))))),sK24(X1,sK20(sK19(sK19(powerset(X0)))))),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_130,c_89261]) ).
tcf(c_89785,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),X1),sK24(sK20(sK19(sK19(powerset(X0)))),X1)),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = X1 )
| ~ empty(X0)
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_130,c_89261]) ).
tcf(c_89787,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8548,c_89261]) ).
tcf(c_89788,plain,
! [X0: $i] :
( element(sK6(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6286,c_89261]) ).
tcf(c_89789,plain,
! [X0: $i] :
( in(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8302,c_89261]) ).
tcf(c_89790,plain,
! [X0: $i] :
( in(sK6(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5335,c_89261]) ).
tcf(c_89791,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK5(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5141,c_89261]) ).
tcf(c_89792,plain,
! [X0: $i] :
( element(sK14(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8430,c_89261]) ).
tcf(c_89793,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_6336,c_89261]) ).
tcf(c_89794,plain,
! [X0: $i] :
( in(sK14(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8298,c_89261]) ).
tcf(c_89795,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK14(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5563,c_89261]) ).
tcf(c_89796,plain,
! [X0: $i] :
( in(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_5542,c_89261]) ).
tcf(c_89797,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8327,c_89261]) ).
tcf(c_89798,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(sK19(sK19(powerset(X0)))),sK1)) = sK23(sK20(sK19(sK19(powerset(X0)))),sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5709,c_89261]) ).
tcf(c_89799,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5669,c_89261]) ).
tcf(c_89800,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8322,c_89261]) ).
tcf(c_89801,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK23(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5704,c_89261]) ).
tcf(c_89802,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5654,c_89261]) ).
tcf(c_89803,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK1))
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8332,c_89261]) ).
tcf(c_89804,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(sK19(sK19(powerset(X0)))),sK1)) = sK21(sK20(sK19(sK19(powerset(X0)))),sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5969,c_89261]) ).
tcf(c_89805,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK2))
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5929,c_89261]) ).
tcf(c_89806,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8337,c_89261]) ).
tcf(c_89807,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK22(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5964,c_89261]) ).
tcf(c_89808,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ~ empty(X0)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5914,c_89261]) ).
tcf(c_89809,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8158,c_89261]) ).
tcf(c_89811,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23755,c_89261]) ).
tcf(c_89812,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18823,c_89261]) ).
tcf(c_89813,plain,
! [X0: $i] :
( in(sK5(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_89261]) ).
tcf(c_89814,plain,
! [X0: $i] :
( in(sK6(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_89261]) ).
tcf(c_89815,plain,
! [X0: $i] :
( in(sK14(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_89261]) ).
tcf(c_89816,plain,
! [X0: $i] :
( in(sK13(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_rng(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_89261]) ).
tcf(c_89817,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23773,c_89261]) ).
tcf(c_89818,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK2) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18841,c_89261]) ).
tcf(c_89819,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(sK19(powerset(X0)))),sK2),relation_dom(sK2))
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23767,c_89261]) ).
tcf(c_89820,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(sK19(powerset(X0)))),sK2),relation_rng(sK2))
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18835,c_89261]) ).
tcf(c_89821,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(sK19(powerset(X0)))),sK2),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23761,c_89261]) ).
tcf(c_89822,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(sK19(powerset(X0)))),sK2),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18829,c_89261]) ).
tcf(c_89823,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73325,c_89261]) ).
tcf(c_89824,plain,
! [X0: $i] :
( empty(sK20(sK19(sK19(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36111,c_89261]) ).
tcf(c_90097,plain,
! [X0: $i,X1: $i] :
( in(sK5(sK20(sK19(sK19(powerset(X0)))),X1),X1)
| element(ordered_pair(sK5(sK20(sK19(sK19(powerset(X0)))),X1),sK6(sK20(sK19(sK19(powerset(X0)))),X1)),X0)
| ( relation_dom(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_77,c_89264]) ).
tcf(c_90098,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,sK7(sK20(sK19(sK19(powerset(X1)))),X0)),X1)
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_dom(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_79,c_89264]) ).
tcf(c_90099,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(X0,apply(sK20(sK19(sK19(powerset(X1)))),X0)),X1)
| ~ function(sK20(sK19(sK19(powerset(X1)))))
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_dom(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_87,c_89264]) ).
tcf(c_90100,plain,
! [X0: $i,X1: $i] :
( in(sK13(sK20(sK19(sK19(powerset(X0)))),X1),X1)
| element(ordered_pair(sK14(sK20(sK19(sK19(powerset(X0)))),X1),sK13(sK20(sK19(sK19(powerset(X0)))),X1)),X0)
| ( relation_rng(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_105,c_89264]) ).
tcf(c_90101,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK15(sK20(sK19(sK19(powerset(X1)))),X0),X0),X1)
| ~ relation(sK20(sK19(sK19(powerset(X1)))))
| ~ in(X0,relation_rng(sK20(sK19(sK19(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_107,c_89264]) ).
tcf(c_90102,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),X1),sK21(sK20(sK19(sK19(powerset(X0)))),X1)),X0)
| in(ordered_pair(sK21(sK20(sK19(sK19(powerset(X0)))),X1),sK22(sK20(sK19(sK19(powerset(X0)))),X1)),X1)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_125,c_89264]) ).
tcf(c_90103,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK21(X1,sK20(sK19(sK19(powerset(X0))))),sK22(X1,sK20(sK19(sK19(powerset(X0)))))),X0)
| in(ordered_pair(sK22(X1,sK20(sK19(sK19(powerset(X0))))),sK21(X1,sK20(sK19(sK19(powerset(X0)))))),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(X1) )
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_125,c_89264]) ).
tcf(c_90104,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(X1,sK20(sK19(sK19(powerset(X0))))),sK24(X1,sK20(sK19(sK19(powerset(X0)))))),X0)
| in(ordered_pair(sK23(X1,sK20(sK19(sK19(powerset(X0))))),sK24(X1,sK20(sK19(sK19(powerset(X0)))))),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_130,c_89264]) ).
tcf(c_90105,plain,
! [X0: $i,X1: $i] :
( element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),X1),sK24(sK20(sK19(sK19(powerset(X0)))),X1)),X0)
| in(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),X1),sK24(sK20(sK19(sK19(powerset(X0)))),X1)),X1)
| ( sK20(sK19(sK19(powerset(X0)))) = X1 )
| ~ relation(X1)
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_130,c_89264]) ).
tcf(c_90106,plain,
! [X0: $i] :
( empty(sK20(sK19(sK19(powerset(X0)))))
| element(sK20(sK20(sK19(sK19(powerset(X0))))),X0) ),
inference(superposition,[status(thm)],[c_3448,c_89264]) ).
tcf(c_90107,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8548,c_89264]) ).
tcf(c_90108,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| element(sK6(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_6286,c_89264]) ).
tcf(c_90109,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_8302,c_89264]) ).
tcf(c_90110,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK6(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) ) ),
inference(superposition,[status(thm)],[c_5335,c_89264]) ).
tcf(c_90111,plain,
! [X0: $i] :
( element(sK5(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK5(sK1,sK20(sK19(sK19(powerset(X0))))) ) ),
inference(superposition,[status(thm)],[c_5141,c_89264]) ).
tcf(c_90112,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| element(sK14(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8430,c_89264]) ).
tcf(c_90113,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_6336,c_89264]) ).
tcf(c_90114,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK14(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_8298,c_89264]) ).
tcf(c_90115,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK14(sK1,sK20(sK19(sK19(powerset(X0))))) ) ),
inference(superposition,[status(thm)],[c_5563,c_89264]) ).
tcf(c_90116,plain,
! [X0: $i] :
( element(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK13(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) ) ),
inference(superposition,[status(thm)],[c_5542,c_89264]) ).
tcf(c_90117,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK1))
| element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),sK1),sK24(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8327,c_89264]) ).
tcf(c_90118,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),sK1),sK24(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK20(sK19(sK19(powerset(X0)))),sK1)) = sK23(sK20(sK19(sK19(powerset(X0)))),sK1) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5709,c_89264]) ).
tcf(c_90119,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),sK1),sK24(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5669,c_89264]) ).
tcf(c_90120,plain,
! [X0: $i] :
( in(sK23(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| element(ordered_pair(sK23(sK1,sK20(sK19(sK19(powerset(X0))))),sK24(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8322,c_89264]) ).
tcf(c_90121,plain,
! [X0: $i] :
( element(ordered_pair(sK23(sK1,sK20(sK19(sK19(powerset(X0))))),sK24(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK23(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5704,c_89264]) ).
tcf(c_90122,plain,
! [X0: $i] :
( in(sK24(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| element(ordered_pair(sK23(sK1,sK20(sK19(sK19(powerset(X0))))),sK24(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5654,c_89264]) ).
tcf(c_90123,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK1))
| element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),sK1),sK21(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8332,c_89264]) ).
tcf(c_90124,plain,
! [X0: $i] :
( element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),sK1),sK21(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK20(sK19(sK19(powerset(X0)))),sK1)) = sK21(sK20(sK19(sK19(powerset(X0)))),sK1) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5969,c_89264]) ).
tcf(c_90125,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(sK19(powerset(X0)))),sK1),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),sK1),sK21(sK20(sK19(sK19(powerset(X0)))),sK1)),X0)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK1 )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5929,c_89264]) ).
tcf(c_90126,plain,
! [X0: $i] :
( in(sK22(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK1))
| element(ordered_pair(sK21(sK1,sK20(sK19(sK19(powerset(X0))))),sK22(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_8337,c_89264]) ).
tcf(c_90127,plain,
! [X0: $i] :
( element(ordered_pair(sK21(sK1,sK20(sK19(sK19(powerset(X0))))),sK22(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK20(sK19(sK19(powerset(X0)))))) = sK22(sK1,sK20(sK19(sK19(powerset(X0))))) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5964,c_89264]) ).
tcf(c_90128,plain,
! [X0: $i] :
( in(sK21(sK1,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| element(ordered_pair(sK21(sK1,sK20(sK19(sK19(powerset(X0))))),sK22(sK1,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK1) )
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_5914,c_89264]) ).
tcf(c_90129,plain,
! [X0: $i] :
( element(sK5(empty_set,sK20(sK19(sK19(powerset(X0))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8158,c_89264]) ).
tcf(c_90130,plain,
! [X0: $i] :
( element(sK13(empty_set,sK20(sK19(sK19(powerset(X0))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_8154,c_89264]) ).
tcf(c_90131,plain,
! [X0: $i] :
( in(sK23(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| element(ordered_pair(sK23(sK2,sK20(sK19(sK19(powerset(X0))))),sK24(sK2,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23755,c_89264]) ).
tcf(c_90132,plain,
! [X0: $i] :
( in(sK24(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| element(ordered_pair(sK23(sK2,sK20(sK19(sK19(powerset(X0))))),sK24(sK2,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18823,c_89264]) ).
tcf(c_90133,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK5(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_89264]) ).
tcf(c_90134,plain,
! [X0: $i] :
( element(sK5(sK2,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK6(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_dom(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_89264]) ).
tcf(c_90135,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK14(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_89264]) ).
tcf(c_90136,plain,
! [X0: $i] :
( element(sK13(sK2,sK20(sK19(sK19(powerset(X0))))),X0)
| in(sK13(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| ( sK20(sK19(sK19(powerset(X0)))) = relation_rng(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_89264]) ).
tcf(c_90137,plain,
! [X0: $i] :
( in(sK22(sK2,sK20(sK19(sK19(powerset(X0))))),relation_dom(sK2))
| element(ordered_pair(sK21(sK2,sK20(sK19(sK19(powerset(X0))))),sK22(sK2,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23773,c_89264]) ).
tcf(c_90138,plain,
! [X0: $i] :
( in(sK21(sK2,sK20(sK19(sK19(powerset(X0))))),relation_rng(sK2))
| element(ordered_pair(sK21(sK2,sK20(sK19(sK19(powerset(X0))))),sK22(sK2,sK20(sK19(sK19(powerset(X0)))))),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18841,c_89264]) ).
tcf(c_90139,plain,
! [X0: $i] :
( in(sK21(sK20(sK19(sK19(powerset(X0)))),sK2),relation_dom(sK2))
| element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),sK2),sK21(sK20(sK19(sK19(powerset(X0)))),sK2)),X0)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23767,c_89264]) ).
tcf(c_90140,plain,
! [X0: $i] :
( in(sK22(sK20(sK19(sK19(powerset(X0)))),sK2),relation_rng(sK2))
| element(ordered_pair(sK22(sK20(sK19(sK19(powerset(X0)))),sK2),sK21(sK20(sK19(sK19(powerset(X0)))),sK2)),X0)
| ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18835,c_89264]) ).
tcf(c_90141,plain,
! [X0: $i] :
( in(sK23(sK20(sK19(sK19(powerset(X0)))),sK2),relation_dom(sK2))
| element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),sK2),sK24(sK20(sK19(sK19(powerset(X0)))),sK2)),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_23761,c_89264]) ).
tcf(c_90142,plain,
! [X0: $i] :
( in(sK24(sK20(sK19(sK19(powerset(X0)))),sK2),relation_rng(sK2))
| element(ordered_pair(sK23(sK20(sK19(sK19(powerset(X0)))),sK2),sK24(sK20(sK19(sK19(powerset(X0)))),sK2)),X0)
| ( sK20(sK19(sK19(powerset(X0)))) = sK2 )
| ~ relation(relation_inverse(sK2))
| ~ relation(sK20(sK19(sK19(powerset(X0))))) ),
inference(superposition,[status(thm)],[c_18829,c_89264]) ).
tcf(c_90143,plain,
! [X0: $i] :
( empty(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))
| element(sK20(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_73325,c_89264]) ).
tcf(c_90144,plain,
! [X0: $i] :
( empty(sK20(sK19(sK19(powerset(X0)))))
| element(sK20(sK19(sK20(sK19(sK19(powerset(X0)))))),X0) ),
inference(superposition,[status(thm)],[c_36111,c_89264]) ).
tcf(c_90145,plain,
! [X0: $i] :
( empty(sK20(sK19(sK19(powerset(X0)))))
| element(sK20(sK19(sK19(sK20(sK19(sK19(powerset(X0))))))),X0) ),
inference(superposition,[status(thm)],[c_89256,c_89264]) ).
tcf(c_90595,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35023]) ).
tcf(c_90596,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35023]) ).
tcf(c_90597,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35023]) ).
tcf(c_90598,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35023]) ).
tcf(c_90599,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35023]) ).
tcf(c_90600,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35023]) ).
tcf(c_90601,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35023]) ).
tcf(c_90602,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35023]) ).
tcf(c_90603,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35023]) ).
tcf(c_90604,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35023]) ).
tcf(c_90605,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35023]) ).
tcf(c_90606,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35023]) ).
tcf(c_90607,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35023]) ).
tcf(c_90608,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35023]) ).
tcf(c_90609,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35023]) ).
tcf(c_90610,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35023]) ).
tcf(c_90800,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35023]) ).
tcf(c_90801,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35022]) ).
tcf(c_90804,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29434]) ).
tcf(c_90805,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29433]) ).
tcf(c_90806,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29432]) ).
tcf(c_90807,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29048]) ).
tcf(c_90808,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29047]) ).
tcf(c_90809,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29046]) ).
tcf(c_90810,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29001]) ).
tcf(c_90811,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_29000]) ).
tcf(c_90812,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_28999]) ).
tcf(c_90813,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(sK19(sK19(powerset(X0)))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12147]) ).
tcf(c_90814,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3853]) ).
tcf(c_90815,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3852]) ).
tcf(c_90816,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3847]) ).
tcf(c_90817,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3813]) ).
tcf(c_90818,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3812]) ).
tcf(c_90819,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3807]) ).
tcf(c_90820,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_39387]) ).
tcf(c_90821,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_39386]) ).
tcf(c_90822,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_39385]) ).
tcf(c_90823,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34275]) ).
tcf(c_90824,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34274]) ).
tcf(c_90825,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34273]) ).
tcf(c_90826,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34257]) ).
tcf(c_90827,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34256]) ).
tcf(c_90828,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_34255]) ).
tcf(c_90829,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_27401]) ).
tcf(c_90830,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_27400]) ).
tcf(c_90831,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_27399]) ).
tcf(c_90832,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25347]) ).
tcf(c_90833,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25346]) ).
tcf(c_90834,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25345]) ).
tcf(c_90835,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25312]) ).
tcf(c_90836,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25311]) ).
tcf(c_90837,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25310]) ).
tcf(c_90838,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25248]) ).
tcf(c_90839,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25247]) ).
tcf(c_90840,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_25246]) ).
tcf(c_90841,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24512]) ).
tcf(c_90842,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24511]) ).
tcf(c_90843,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24510]) ).
tcf(c_90844,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24398]) ).
tcf(c_90845,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24397]) ).
tcf(c_90846,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24396]) ).
tcf(c_90847,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24361]) ).
tcf(c_90848,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24360]) ).
tcf(c_90849,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24359]) ).
tcf(c_90850,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24299]) ).
tcf(c_90851,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24298]) ).
tcf(c_90852,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_24297]) ).
tcf(c_90853,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23557]) ).
tcf(c_90854,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23556]) ).
tcf(c_90855,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23555]) ).
tcf(c_90856,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23520]) ).
tcf(c_90857,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23519]) ).
tcf(c_90858,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23518]) ).
tcf(c_90859,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23406]) ).
tcf(c_90860,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23405]) ).
tcf(c_90861,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23404]) ).
tcf(c_90862,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23371]) ).
tcf(c_90863,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23370]) ).
tcf(c_90864,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_23369]) ).
tcf(c_90865,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_22305]) ).
tcf(c_90866,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_22304]) ).
tcf(c_90867,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_22303]) ).
tcf(c_90868,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_21079]) ).
tcf(c_90869,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_21078]) ).
tcf(c_90870,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_21077]) ).
tcf(c_90871,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20790]) ).
tcf(c_90872,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20789]) ).
tcf(c_90873,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20788]) ).
tcf(c_90874,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20733]) ).
tcf(c_90875,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20732]) ).
tcf(c_90876,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20731]) ).
tcf(c_90877,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14787]) ).
tcf(c_90878,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20567]) ).
tcf(c_90879,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20566]) ).
tcf(c_90880,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_20565]) ).
tcf(c_90881,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19623]) ).
tcf(c_90882,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14242]) ).
tcf(c_90883,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14162]) ).
tcf(c_90884,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14077]) ).
tcf(c_90885,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12144]) ).
tcf(c_90886,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19622]) ).
tcf(c_90887,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19621]) ).
tcf(c_90888,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12143]) ).
tcf(c_90889,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12142]) ).
tcf(c_90890,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12141]) ).
tcf(c_90891,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12140]) ).
tcf(c_90892,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19044]) ).
tcf(c_90893,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19043]) ).
tcf(c_90894,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12139]) ).
tcf(c_90895,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_19042]) ).
tcf(c_90896,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18986]) ).
tcf(c_90897,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18985]) ).
tcf(c_90898,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18984]) ).
tcf(c_90899,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_36589]) ).
tcf(c_90900,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18933]) ).
tcf(c_90901,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18932]) ).
tcf(c_90902,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18931]) ).
tcf(c_90903,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18887]) ).
tcf(c_90904,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18886]) ).
tcf(c_90905,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18885]) ).
tcf(c_90906,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18057]) ).
tcf(c_90907,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18056]) ).
tcf(c_90908,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_18055]) ).
tcf(c_90909,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17694]) ).
tcf(c_90910,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17693]) ).
tcf(c_90911,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17692]) ).
tcf(c_90912,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17624]) ).
tcf(c_90913,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17623]) ).
tcf(c_90914,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17622]) ).
tcf(c_90915,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17580]) ).
tcf(c_90916,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17579]) ).
tcf(c_90917,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17578]) ).
tcf(c_90918,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17545]) ).
tcf(c_90919,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17544]) ).
tcf(c_90920,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_17543]) ).
tcf(c_90921,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_16055]) ).
tcf(c_90922,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_16054]) ).
tcf(c_90923,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_16053]) ).
tcf(c_90924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15952]) ).
tcf(c_90925,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15951]) ).
tcf(c_90926,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15950]) ).
tcf(c_90927,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15917]) ).
tcf(c_90928,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15916]) ).
tcf(c_90929,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15915]) ).
tcf(c_90930,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15880]) ).
tcf(c_90931,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15879]) ).
tcf(c_90932,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_15878]) ).
tcf(c_90933,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12149]) ).
tcf(c_90934,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12148]) ).
tcf(c_90935,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11026]) ).
tcf(c_90936,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11025]) ).
tcf(c_90937,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11024]) ).
tcf(c_90938,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3663]) ).
tcf(c_90939,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3662]) ).
tcf(c_90940,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(sK19(sK19(powerset(X0))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3661]) ).
tcf(c_90941,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = relation_rng(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3632]) ).
tcf(c_90942,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12146]) ).
tcf(c_90943,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = relation_inverse(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3631]) ).
tcf(c_90944,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = relation_dom(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3626]) ).
tcf(c_90945,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14780]) ).
tcf(c_90946,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14779]) ).
tcf(c_90947,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14778]) ).
tcf(c_90948,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14235]) ).
tcf(c_90949,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14234]) ).
tcf(c_90950,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14233]) ).
tcf(c_90951,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14155]) ).
tcf(c_90952,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14154]) ).
tcf(c_90953,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14153]) ).
tcf(c_90954,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14070]) ).
tcf(c_90955,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14069]) ).
tcf(c_90956,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_14068]) ).
tcf(c_90957,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11811]) ).
tcf(c_90958,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11810]) ).
tcf(c_90959,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11809]) ).
tcf(c_90960,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11771]) ).
tcf(c_90961,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11770]) ).
tcf(c_90962,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11769]) ).
tcf(c_90963,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11729]) ).
tcf(c_90964,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11728]) ).
tcf(c_90965,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11727]) ).
tcf(c_90966,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11691]) ).
tcf(c_90967,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11690]) ).
tcf(c_90968,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11689]) ).
tcf(c_90969,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11660]) ).
tcf(c_90970,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11659]) ).
tcf(c_90971,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11658]) ).
tcf(c_90972,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11297]) ).
tcf(c_90973,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11296]) ).
tcf(c_90974,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_11295]) ).
tcf(c_90975,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_12150]) ).
tcf(c_90976,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_9831]) ).
tcf(c_90977,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_9830]) ).
tcf(c_90978,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_9829]) ).
tcf(c_90979,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3423]) ).
tcf(c_90980,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3422]) ).
tcf(c_90981,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3421]) ).
tcf(c_90982,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3403]) ).
tcf(c_90983,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3402]) ).
tcf(c_90984,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3401]) ).
tcf(c_90985,plain,
! [X0: $i] :
( ( function_inverse(sK20(sK19(sK19(powerset(X0))))) = relation_inverse(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_957]) ).
tcf(c_90986,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3333]) ).
tcf(c_90987,plain,
! [X0: $i,X1: $i] :
( ( sK20(sK19(sK19(powerset(X0)))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_66]) ).
tcf(c_90988,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3330]) ).
tcf(c_90989,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(sK19(powerset(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_3327]) ).
tcf(c_90991,plain,
! [X0: $i] :
( relation(sK20(sK19(sK19(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_94]) ).
tcf(c_90992,plain,
! [X0: $i] :
( function(sK20(sK19(sK19(powerset(X0)))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_85]) ).
tcf(c_91763,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = relation_dom(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_90991,c_72]) ).
tcf(c_91764,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = relation_rng(sK20(sK19(sK19(powerset(X0))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_90991,c_71]) ).
tcf(c_91765,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0)))))) = sK20(sK19(sK19(powerset(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_90991,c_120]) ).
tcf(c_91780,plain,
( empty(sK20(powerset(empty_set)))
| element(sK20(sK19(empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_14781,c_36527]) ).
tcf(c_91781,plain,
! [X0: $i] :
( empty(X0)
| empty(sK20(powerset(X0)))
| in(sK20(sK19(sK20(powerset(X0)))),X0) ),
inference(superposition,[status(thm)],[c_36527,c_68]) ).
tcf(c_91782,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| empty(sK20(powerset(powerset(X1))))
| ~ in(X0,sK20(sK19(sK20(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_36527,c_114]) ).
tcf(c_91783,plain,
! [X0: $i,X1: $i] :
( empty(sK20(powerset(powerset(X1))))
| ~ empty(X1)
| ~ in(X0,sK20(sK19(sK20(powerset(powerset(X1)))))) ),
inference(superposition,[status(thm)],[c_36527,c_113]) ).
tcf(c_91784,plain,
( empty(empty_set)
| element(sK20(sK19(empty_set)),empty_set) ),
inference(light_normalisation,[status(thm)],[c_91780,c_14781]) ).
tcf(c_91810,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK2,X0)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_12604]) ).
tcf(c_91811,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_12604]) ).
tcf(c_91812,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(relation_inverse(sK1),sK21(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12791,c_12604]) ).
tcf(c_91813,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_12604]) ).
tcf(c_91816,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10201,c_12604]) ).
tcf(c_91817,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_12604]) ).
tcf(c_91819,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK7(relation_inverse(sK1),sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_12604]) ).
tcf(c_91820,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),sK7(relation_inverse(sK1),apply(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_12604]) ).
tcf(c_91821,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_12604]) ).
tcf(c_91822,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(relation_inverse(sK1),sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10226,c_12604]) ).
tcf(c_91823,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(relation_inverse(sK1),sK21(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10228,c_12604]) ).
tcf(c_91825,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK7(relation_inverse(sK1),sK13(sK1,empty_set))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10231,c_12604]) ).
tcf(c_91826,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12764,c_12604]) ).
tcf(c_91827,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_12604]) ).
tcf(c_91828,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),apply(relation_inverse(sK1),sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_12604]) ).
tcf(c_91829,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_12604]) ).
tcf(c_91830,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(relation_inverse(sK1),sK22(sK1,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12789,c_12604]) ).
tcf(c_91831,plain,
( in(ordered_pair(sK13(sK1,empty_set),apply(relation_inverse(sK1),sK13(sK1,empty_set))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12794,c_12604]) ).
tcf(c_91832,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_12604]) ).
tcf(c_91833,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_12604]) ).
tcf(c_91834,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_12604]) ).
tcf(c_91835,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_12604]) ).
tcf(c_91839,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK15(sK1,sK7(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_12604]) ).
tcf(c_91845,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1))
| ~ in(relation_inverse(sK1),ordered_pair(apply(sK1,X0),X0)) ),
inference(superposition,[status(thm)],[c_12604,c_70]) ).
tcf(c_91846,plain,
! [X0: $i] :
( element(ordered_pair(apply(sK1,X0),X0),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12604,c_69]) ).
tcf(c_91848,plain,
! [X0: $i] :
( in(X0,relation_rng(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12604,c_106]) ).
tcf(c_91849,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12604,c_78]) ).
tcf(c_91851,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK1)) = X0 )
| ( apply(sK1,sK13(relation_inverse(sK1),X0)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(sK13(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12604,c_104]) ).
tcf(c_91861,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91849,c_4030]) ).
tcf(c_91887,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK13(relation_inverse(sK1),X0)) = empty_set )
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(sK13(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91851,c_3821]) ).
tcf(c_91888,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK13(relation_inverse(sK1),X0)) = empty_set )
| ~ in(sK13(relation_inverse(sK1),X0),X0)
| ~ in(sK13(relation_inverse(sK1),X0),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91887,c_3611]) ).
tcf(c_92017,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),sK5(sK1,X0)) ),
inference(superposition,[status(thm)],[c_12635,c_70]) ).
tcf(c_92021,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12635,c_12766]) ).
tcf(c_92022,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12635,c_12765]) ).
tcf(c_92023,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,X0)))) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12635,c_10203]) ).
tcf(c_92024,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0)))) = sK7(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12635,c_10202]) ).
tcf(c_92025,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK15(sK1,apply(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_12635,c_6249]) ).
tcf(c_92026,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK15(sK1,sK7(sK1,sK5(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_12635,c_5349]) ).
tcf(c_92028,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK1),sK5(sK1,X0)) = apply(sK1,sK5(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12635,c_12284]) ).
tcf(c_92029,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12635,c_4619]) ).
tcf(c_92030,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12635,c_4406]) ).
tcf(c_92084,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),sK6(sK1,X0)) ),
inference(superposition,[status(thm)],[c_12636,c_70]) ).
tcf(c_92088,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,X0))) = apply(sK1,sK15(sK1,sK6(sK1,X0))) ) ),
inference(superposition,[status(thm)],[c_12636,c_12335]) ).
tcf(c_92089,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12636,c_8396]) ).
tcf(c_92090,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,X0)))) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12636,c_8395]) ).
tcf(c_92091,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,apply(sK2,sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12636,c_4044]) ).
tcf(c_92092,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( sK15(relation_inverse(sK2),sK6(sK1,X0)) = apply(sK2,sK6(sK1,X0)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_12636,c_42224]) ).
tcf(c_92093,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12636,c_12701]) ).
tcf(c_92094,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12636,c_10144]) ).
tcf(c_92095,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,X0)) = sK15(sK1,sK6(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_12636,c_4468]) ).
tcf(c_92140,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35024]) ).
tcf(c_92141,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35024]) ).
tcf(c_92142,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35024]) ).
tcf(c_92143,plain,
relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35024]) ).
tcf(c_92144,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35024]) ).
tcf(c_92145,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35024]) ).
tcf(c_92146,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35024]) ).
tcf(c_92147,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35024]) ).
tcf(c_92148,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35024]) ).
tcf(c_92149,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35024]) ).
tcf(c_92150,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35024]) ).
tcf(c_92151,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35024]) ).
tcf(c_92152,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35024]) ).
tcf(c_92153,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35024]) ).
tcf(c_92154,plain,
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35024]) ).
tcf(c_92155,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35024]) ).
tcf(c_92156,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35024]) ).
tcf(c_92310,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35040]) ).
tcf(c_92311,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35040]) ).
tcf(c_92312,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35040]) ).
tcf(c_92313,plain,
relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35040]) ).
tcf(c_92314,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35040]) ).
tcf(c_92315,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35040]) ).
tcf(c_92316,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35040]) ).
tcf(c_92317,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35040]) ).
tcf(c_92318,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35040]) ).
tcf(c_92319,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35040]) ).
tcf(c_92320,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35040]) ).
tcf(c_92321,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35040]) ).
tcf(c_92322,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35040]) ).
tcf(c_92323,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35040]) ).
tcf(c_92324,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35040]) ).
tcf(c_92325,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35040]) ).
tcf(c_92326,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35040]) ).
tcf(c_92364,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35041]) ).
tcf(c_92365,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35041]) ).
tcf(c_92366,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35041]) ).
tcf(c_92367,plain,
relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35041]) ).
tcf(c_92368,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35041]) ).
tcf(c_92369,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35041]) ).
tcf(c_92370,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35041]) ).
tcf(c_92371,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35041]) ).
tcf(c_92372,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35041]) ).
tcf(c_92373,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35041]) ).
tcf(c_92374,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35041]) ).
tcf(c_92375,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35041]) ).
tcf(c_92376,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35041]) ).
tcf(c_92377,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35041]) ).
tcf(c_92378,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35041]) ).
tcf(c_92379,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35041]) ).
tcf(c_92380,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35041]) ).
tcf(c_92475,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35042]) ).
tcf(c_92476,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35042]) ).
tcf(c_92477,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35042]) ).
tcf(c_92478,plain,
relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35042]) ).
tcf(c_92479,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35042]) ).
tcf(c_92480,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35042]) ).
tcf(c_92481,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35042]) ).
tcf(c_92482,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35042]) ).
tcf(c_92483,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35042]) ).
tcf(c_92484,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35042]) ).
tcf(c_92485,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35042]) ).
tcf(c_92486,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35042]) ).
tcf(c_92487,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35042]) ).
tcf(c_92488,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35042]) ).
tcf(c_92489,plain,
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35042]) ).
tcf(c_92490,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35042]) ).
tcf(c_92491,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35042]) ).
tcf(c_92587,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37368]) ).
tcf(c_92588,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37368]) ).
tcf(c_92589,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37368]) ).
tcf(c_92590,plain,
relation_inverse(sK20(sK19(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37368]) ).
tcf(c_92591,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37368]) ).
tcf(c_92592,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37368]) ).
tcf(c_92593,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37368]) ).
tcf(c_92594,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37368]) ).
tcf(c_92595,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37368]) ).
tcf(c_92596,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37368]) ).
tcf(c_92597,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37368]) ).
tcf(c_92598,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37368]) ).
tcf(c_92599,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37368]) ).
tcf(c_92600,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37368]) ).
tcf(c_92601,plain,
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37368]) ).
tcf(c_92602,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37368]) ).
tcf(c_92603,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37368]) ).
tcf(c_92695,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37370]) ).
tcf(c_92696,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37370]) ).
tcf(c_92697,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37370]) ).
tcf(c_92698,plain,
relation_rng(sK20(sK19(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37370]) ).
tcf(c_92699,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37370]) ).
tcf(c_92700,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37370]) ).
tcf(c_92701,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37370]) ).
tcf(c_92702,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37370]) ).
tcf(c_92703,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37370]) ).
tcf(c_92704,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37370]) ).
tcf(c_92705,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37370]) ).
tcf(c_92706,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37370]) ).
tcf(c_92707,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37370]) ).
tcf(c_92708,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37370]) ).
tcf(c_92709,plain,
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37370]) ).
tcf(c_92710,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37370]) ).
tcf(c_92711,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37370]) ).
tcf(c_92749,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37371]) ).
tcf(c_92750,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37371]) ).
tcf(c_92751,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37371]) ).
tcf(c_92752,plain,
relation_dom(sK20(sK19(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37371]) ).
tcf(c_92753,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37371]) ).
tcf(c_92754,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37371]) ).
tcf(c_92755,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37371]) ).
tcf(c_92756,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37371]) ).
tcf(c_92757,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37371]) ).
tcf(c_92758,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37371]) ).
tcf(c_92759,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37371]) ).
tcf(c_92760,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37371]) ).
tcf(c_92761,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37371]) ).
tcf(c_92762,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37371]) ).
tcf(c_92763,plain,
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37371]) ).
tcf(c_92764,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37371]) ).
tcf(c_92765,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37371]) ).
tcf(c_92871,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_89,c_13471]) ).
tcf(c_92872,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,apply(sK1,apply(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_57900,c_13471]) ).
tcf(c_92873,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK2,sK7(sK1,apply(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_56474,c_13471]) ).
tcf(c_92875,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),sK7(sK1,X0))
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_55855,c_13471]) ).
tcf(c_92879,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),apply(sK1,X0))
| ~ in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56725,c_13471]) ).
tcf(c_92883,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK2,sK6(sK1,X0)) = empty_set )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK2),sK6(sK1,X0))
| ~ in(sK5(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12637,c_13471]) ).
tcf(c_92884,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(relation_dom(sK2),sK6(sK1,relation_dom(sK2)))
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5251,c_13471]) ).
tcf(c_92885,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(relation_dom(sK2),sK5(sK1,relation_dom(sK2)))
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13935,c_13471]) ).
tcf(c_92886,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(relation_dom(sK2),sK5(sK1,relation_dom(sK2)))
| ~ in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13933,c_13471]) ).
tcf(c_92887,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),sK5(sK1,relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_12634,c_13471]) ).
tcf(c_92889,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(relation_dom(sK2),sK22(sK1,sK1))
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18307,c_13471]) ).
tcf(c_92890,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1))
| ~ in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18305,c_13471]) ).
tcf(c_92891,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK22(sK1,sK1)) = empty_set )
| ~ in(relation_dom(sK2),sK22(sK1,sK1))
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_17971,c_13471]) ).
tcf(c_92892,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7241,c_13471]) ).
tcf(c_92893,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1))
| ~ in(sK15(sK1,sK21(sK1,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7060,c_13471]) ).
tcf(c_92894,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1))
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_7472,c_13471]) ).
tcf(c_92895,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK13(sK1,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_6420,c_13471]) ).
tcf(c_92896,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK13(sK1,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_6421,c_13471]) ).
tcf(c_92897,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ~ in(relation_dom(sK2),sK13(sK1,empty_set))
| ~ in(sK15(sK1,sK13(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9987,c_13471]) ).
tcf(c_92898,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(sK1,empty_set)) = empty_set )
| ~ in(relation_dom(sK2),sK13(sK1,empty_set))
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8130,c_13471]) ).
tcf(c_92903,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK15(sK1,X0))) ),
inference(superposition,[status(thm)],[c_58270,c_13471]) ).
tcf(c_92904,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK2,sK7(sK1,sK15(sK1,X0))) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK15(sK1,X0))) ),
inference(superposition,[status(thm)],[c_59117,c_13471]) ).
tcf(c_92905,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_8770,c_13471]) ).
tcf(c_92906,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK21(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_8771,c_13471]) ).
tcf(c_92907,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_8797,c_13471]) ).
tcf(c_92908,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK22(sK1,sK1))) ),
inference(superposition,[status(thm)],[c_8798,c_13471]) ).
tcf(c_92909,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK14(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_10032,c_13471]) ).
tcf(c_92910,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK7(sK1,sK14(sK1,empty_set))) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK14(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_10033,c_13471]) ).
tcf(c_92913,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK13(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(relation_dom(sK2),sK13(empty_set,relation_dom(sK2)))
| ~ in(sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13387,c_13471]) ).
tcf(c_92916,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK2,sK5(empty_set,relation_dom(sK2))) = empty_set )
| ~ in(relation_dom(sK2),sK5(empty_set,relation_dom(sK2)))
| ~ in(sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14034,c_13471]) ).
tcf(c_92924,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_70881,c_13471]) ).
tcf(c_92925,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_71034,c_13471]) ).
tcf(c_92926,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_71035,c_13471]) ).
tcf(c_92951,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_92871,c_65,c_64]) ).
tcf(c_93215,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_92951]) ).
tcf(c_93216,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_92951]) ).
tcf(c_93217,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_92951]) ).
tcf(c_93218,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_92951]) ).
tcf(c_93220,plain,
( ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_92951]) ).
tcf(c_93222,plain,
( ( apply(sK2,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_92951]) ).
tcf(c_93226,plain,
( ( apply(sK1,empty_set) = empty_set )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK2))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_93218,c_70881]) ).
tcf(c_93317,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35058]) ).
tcf(c_93318,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35058]) ).
tcf(c_93319,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35058]) ).
tcf(c_93320,plain,
relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35058]) ).
tcf(c_93321,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35058]) ).
tcf(c_93322,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35058]) ).
tcf(c_93323,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35058]) ).
tcf(c_93324,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35058]) ).
tcf(c_93325,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35058]) ).
tcf(c_93326,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35058]) ).
tcf(c_93327,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35058]) ).
tcf(c_93328,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35058]) ).
tcf(c_93329,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35058]) ).
tcf(c_93330,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35058]) ).
tcf(c_93331,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35058]) ).
tcf(c_93332,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35058]) ).
tcf(c_93333,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35058]) ).
tcf(c_93413,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35059]) ).
tcf(c_93414,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35059]) ).
tcf(c_93415,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35059]) ).
tcf(c_93416,plain,
relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35059]) ).
tcf(c_93417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35059]) ).
tcf(c_93418,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35059]) ).
tcf(c_93419,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35059]) ).
tcf(c_93420,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35059]) ).
tcf(c_93421,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35059]) ).
tcf(c_93422,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35059]) ).
tcf(c_93423,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35059]) ).
tcf(c_93424,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35059]) ).
tcf(c_93425,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35059]) ).
tcf(c_93426,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35059]) ).
tcf(c_93427,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35059]) ).
tcf(c_93428,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35059]) ).
tcf(c_93429,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35059]) ).
tcf(c_93490,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35060]) ).
tcf(c_93491,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35060]) ).
tcf(c_93492,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35060]) ).
tcf(c_93493,plain,
relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35060]) ).
tcf(c_93494,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35060]) ).
tcf(c_93495,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35060]) ).
tcf(c_93496,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35060]) ).
tcf(c_93497,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35060]) ).
tcf(c_93498,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35060]) ).
tcf(c_93499,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35060]) ).
tcf(c_93500,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35060]) ).
tcf(c_93501,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35060]) ).
tcf(c_93502,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35060]) ).
tcf(c_93503,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35060]) ).
tcf(c_93504,plain,
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35060]) ).
tcf(c_93505,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35060]) ).
tcf(c_93506,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35060]) ).
tcf(c_93823,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35186]) ).
tcf(c_93824,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35186]) ).
tcf(c_93825,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35186]) ).
tcf(c_93826,plain,
relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35186]) ).
tcf(c_93827,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35186]) ).
tcf(c_93828,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35186]) ).
tcf(c_93829,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35186]) ).
tcf(c_93830,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35186]) ).
tcf(c_93831,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35186]) ).
tcf(c_93832,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35186]) ).
tcf(c_93833,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35186]) ).
tcf(c_93834,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35186]) ).
tcf(c_93835,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35186]) ).
tcf(c_93836,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35186]) ).
tcf(c_93837,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35186]) ).
tcf(c_93838,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35186]) ).
tcf(c_93839,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35186]) ).
tcf(c_93877,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35187]) ).
tcf(c_93878,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35187]) ).
tcf(c_93879,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35187]) ).
tcf(c_93880,plain,
relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35187]) ).
tcf(c_93881,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35187]) ).
tcf(c_93882,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35187]) ).
tcf(c_93883,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35187]) ).
tcf(c_93884,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35187]) ).
tcf(c_93885,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35187]) ).
tcf(c_93886,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35187]) ).
tcf(c_93887,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35187]) ).
tcf(c_93888,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35187]) ).
tcf(c_93889,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35187]) ).
tcf(c_93890,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35187]) ).
tcf(c_93891,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35187]) ).
tcf(c_93892,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35187]) ).
tcf(c_93893,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35187]) ).
tcf(c_94151,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35188]) ).
tcf(c_94152,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35188]) ).
tcf(c_94153,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35188]) ).
tcf(c_94154,plain,
relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35188]) ).
tcf(c_94155,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35188]) ).
tcf(c_94156,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35188]) ).
tcf(c_94157,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35188]) ).
tcf(c_94158,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35188]) ).
tcf(c_94159,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35188]) ).
tcf(c_94160,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35188]) ).
tcf(c_94161,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35188]) ).
tcf(c_94162,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35188]) ).
tcf(c_94163,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35188]) ).
tcf(c_94164,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35188]) ).
tcf(c_94165,plain,
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35188]) ).
tcf(c_94166,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35188]) ).
tcf(c_94167,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35188]) ).
tcf(c_94322,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35233]) ).
tcf(c_94323,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35233]) ).
tcf(c_94324,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35233]) ).
tcf(c_94325,plain,
relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35233]) ).
tcf(c_94326,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35233]) ).
tcf(c_94327,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35233]) ).
tcf(c_94328,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35233]) ).
tcf(c_94329,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35233]) ).
tcf(c_94330,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35233]) ).
tcf(c_94331,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35233]) ).
tcf(c_94332,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35233]) ).
tcf(c_94333,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35233]) ).
tcf(c_94334,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35233]) ).
tcf(c_94335,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35233]) ).
tcf(c_94336,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35233]) ).
tcf(c_94337,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35233]) ).
tcf(c_94338,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35233]) ).
tcf(c_94376,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35234]) ).
tcf(c_94377,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35234]) ).
tcf(c_94378,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35234]) ).
tcf(c_94379,plain,
relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35234]) ).
tcf(c_94380,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35234]) ).
tcf(c_94381,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35234]) ).
tcf(c_94382,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35234]) ).
tcf(c_94383,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35234]) ).
tcf(c_94384,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35234]) ).
tcf(c_94385,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35234]) ).
tcf(c_94386,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35234]) ).
tcf(c_94387,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35234]) ).
tcf(c_94388,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35234]) ).
tcf(c_94389,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35234]) ).
tcf(c_94390,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35234]) ).
tcf(c_94391,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35234]) ).
tcf(c_94392,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35234]) ).
tcf(c_94494,plain,
! [X0: $i] :
( in(sK23(relation_dom(X0),sK1),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_29872,c_74,c_29872]) ).
tcf(c_94505,plain,
( in(sK23(relation_rng(sK9),sK1),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_94494]) ).
tcf(c_94507,plain,
( in(sK23(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_94494]) ).
tcf(c_94508,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(relation_dom(X0),sK1)) ),
inference(superposition,[status(thm)],[c_94494,c_70]) ).
tcf(c_94509,plain,
! [X0: $i] :
( element(sK23(relation_dom(X0),sK1),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_69]) ).
tcf(c_94512,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(relation_dom(X0),sK1)))) = apply(sK1,sK23(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_12766]) ).
tcf(c_94513,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(relation_dom(X0),sK1)))) = sK7(sK1,sK23(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_12765]) ).
tcf(c_94514,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(relation_dom(X0),sK1)))) = apply(sK1,sK23(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_10203]) ).
tcf(c_94515,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(relation_dom(X0),sK1)))) = sK7(sK1,sK23(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_10202]) ).
tcf(c_94516,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(relation_dom(X0),sK1))) = sK15(sK1,apply(sK1,sK23(relation_dom(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_6249]) ).
tcf(c_94517,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(relation_dom(X0),sK1))) = sK15(sK1,sK7(sK1,sK23(relation_dom(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_5349]) ).
tcf(c_94519,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK23(relation_dom(X0),sK1)) = apply(sK1,sK23(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_12284]) ).
tcf(c_94520,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(relation_dom(X0),sK1))) = sK23(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_4619]) ).
tcf(c_94521,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(relation_dom(X0),sK1))) = sK23(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_4406]) ).
tcf(c_94528,plain,
( in(sK23(relation_rng(sK12),sK1),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_94507,c_3810]) ).
tcf(c_94532,plain,
( in(sK23(relation_rng(sK9),sK1),relation_dom(sK1))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_94505,c_3808]) ).
tcf(c_94567,plain,
! [X0: $i] :
( in(sK24(relation_dom(X0),sK1),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_29874,c_74,c_29874]) ).
tcf(c_94578,plain,
( in(sK24(relation_rng(sK9),sK1),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_94567]) ).
tcf(c_94580,plain,
( in(sK24(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_94567]) ).
tcf(c_94581,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(relation_dom(X0),sK1)) ),
inference(superposition,[status(thm)],[c_94567,c_70]) ).
tcf(c_94582,plain,
! [X0: $i] :
( element(sK24(relation_dom(X0),sK1),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_69]) ).
tcf(c_94585,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(relation_dom(X0),sK1))) = apply(sK1,sK15(sK1,sK24(relation_dom(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_12335]) ).
tcf(c_94586,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(relation_dom(X0),sK1)))) = sK15(sK1,sK24(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_8396]) ).
tcf(c_94587,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(relation_dom(X0),sK1)))) = sK15(sK1,sK24(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_8395]) ).
tcf(c_94588,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK24(relation_dom(X0),sK1))) = sK24(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_4044]) ).
tcf(c_94589,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(relation_dom(X0),sK1)) = apply(sK2,sK24(relation_dom(X0),sK1)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_94567,c_42224]) ).
tcf(c_94590,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(relation_dom(X0),sK1))) = sK24(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_12701]) ).
tcf(c_94591,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(relation_dom(X0),sK1))) = sK24(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_10144]) ).
tcf(c_94592,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(X0),sK1)) = sK15(sK1,sK24(relation_dom(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94567,c_4468]) ).
tcf(c_94599,plain,
( in(sK24(relation_rng(sK12),sK1),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_94580,c_3810]) ).
tcf(c_94603,plain,
( in(sK24(relation_rng(sK9),sK1),relation_dom(sK2))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_94578,c_3808]) ).
tcf(c_94633,plain,
! [X0: $i] :
( in(sK23(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_29876,c_74,c_29876]) ).
tcf(c_94644,plain,
( in(sK23(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_94633]) ).
tcf(c_94646,plain,
( in(sK23(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_dom(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_94633]) ).
tcf(c_94647,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_94633,c_70]) ).
tcf(c_94648,plain,
! [X0: $i] :
( element(sK23(sK1,relation_dom(X0)),relation_dom(sK1))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_69]) ).
tcf(c_94651,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_dom(X0))))) = apply(sK1,sK23(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_12766]) ).
tcf(c_94652,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_dom(X0))))) = sK7(sK1,sK23(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_12765]) ).
tcf(c_94653,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_dom(X0))))) = apply(sK1,sK23(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_10203]) ).
tcf(c_94654,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_dom(X0))))) = sK7(sK1,sK23(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_10202]) ).
tcf(c_94655,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_dom(X0)))) = sK15(sK1,apply(sK1,sK23(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_6249]) ).
tcf(c_94656,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_dom(X0)))) = sK15(sK1,sK7(sK1,sK23(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_5349]) ).
tcf(c_94658,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK23(sK1,relation_dom(X0))) = apply(sK1,sK23(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_12284]) ).
tcf(c_94659,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_dom(X0)))) = sK23(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_4619]) ).
tcf(c_94660,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_dom(X0)))) = sK23(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_4406]) ).
tcf(c_94667,plain,
( in(sK23(sK1,relation_rng(sK12)),relation_dom(sK1))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_94646,c_3810]) ).
tcf(c_94671,plain,
( in(sK23(sK1,relation_rng(sK9)),relation_dom(sK1))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_94644,c_3808]) ).
tcf(c_94712,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35235]) ).
tcf(c_94713,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35235]) ).
tcf(c_94714,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35235]) ).
tcf(c_94715,plain,
relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35235]) ).
tcf(c_94716,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35235]) ).
tcf(c_94717,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35235]) ).
tcf(c_94718,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35235]) ).
tcf(c_94719,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35235]) ).
tcf(c_94720,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35235]) ).
tcf(c_94721,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35235]) ).
tcf(c_94722,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35235]) ).
tcf(c_94723,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35235]) ).
tcf(c_94724,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35235]) ).
tcf(c_94725,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35235]) ).
tcf(c_94726,plain,
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35235]) ).
tcf(c_94727,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35235]) ).
tcf(c_94728,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35235]) ).
tcf(c_94922,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35251]) ).
tcf(c_94923,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35251]) ).
tcf(c_94924,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35251]) ).
tcf(c_94925,plain,
relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35251]) ).
tcf(c_94926,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35251]) ).
tcf(c_94927,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35251]) ).
tcf(c_94928,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35251]) ).
tcf(c_94929,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35251]) ).
tcf(c_94930,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35251]) ).
tcf(c_94931,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35251]) ).
tcf(c_94932,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35251]) ).
tcf(c_94933,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35251]) ).
tcf(c_94934,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35251]) ).
tcf(c_94935,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35251]) ).
tcf(c_94936,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35251]) ).
tcf(c_94937,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35251]) ).
tcf(c_94938,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35251]) ).
tcf(c_95108,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35252]) ).
tcf(c_95109,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35252]) ).
tcf(c_95110,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35252]) ).
tcf(c_95111,plain,
relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35252]) ).
tcf(c_95112,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35252]) ).
tcf(c_95113,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35252]) ).
tcf(c_95114,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35252]) ).
tcf(c_95115,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35252]) ).
tcf(c_95116,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35252]) ).
tcf(c_95117,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35252]) ).
tcf(c_95118,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35252]) ).
tcf(c_95119,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35252]) ).
tcf(c_95120,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35252]) ).
tcf(c_95121,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35252]) ).
tcf(c_95122,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35252]) ).
tcf(c_95123,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35252]) ).
tcf(c_95124,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35252]) ).
tcf(c_95162,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35253]) ).
tcf(c_95163,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35253]) ).
tcf(c_95164,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35253]) ).
tcf(c_95165,plain,
relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35253]) ).
tcf(c_95166,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35253]) ).
tcf(c_95167,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35253]) ).
tcf(c_95168,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35253]) ).
tcf(c_95169,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35253]) ).
tcf(c_95170,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35253]) ).
tcf(c_95171,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35253]) ).
tcf(c_95172,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35253]) ).
tcf(c_95173,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35253]) ).
tcf(c_95174,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35253]) ).
tcf(c_95175,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35253]) ).
tcf(c_95176,plain,
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35253]) ).
tcf(c_95177,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35253]) ).
tcf(c_95178,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35253]) ).
tcf(c_95380,plain,
! [X0: $i] :
( in(sK24(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_29878,c_74,c_29878]) ).
tcf(c_95391,plain,
( in(sK24(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_95380]) ).
tcf(c_95393,plain,
( in(sK24(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_dom(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_95380]) ).
tcf(c_95394,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(sK1,relation_dom(X0))) ),
inference(superposition,[status(thm)],[c_95380,c_70]) ).
tcf(c_95395,plain,
! [X0: $i] :
( element(sK24(sK1,relation_dom(X0)),relation_dom(sK2))
| ( relation_dom(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_69]) ).
tcf(c_95398,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,relation_dom(X0)))) = apply(sK1,sK15(sK1,sK24(sK1,relation_dom(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_12335]) ).
tcf(c_95399,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,relation_dom(X0))))) = sK15(sK1,sK24(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_8396]) ).
tcf(c_95400,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,relation_dom(X0))))) = sK15(sK1,sK24(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_8395]) ).
tcf(c_95401,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK24(sK1,relation_dom(X0)))) = sK24(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_4044]) ).
tcf(c_95402,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,relation_dom(X0))) = apply(sK2,sK24(sK1,relation_dom(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_95380,c_42224]) ).
tcf(c_95403,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,relation_dom(X0)))) = sK24(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_12701]) ).
tcf(c_95404,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,relation_dom(X0)))) = sK24(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_10144]) ).
tcf(c_95405,plain,
! [X0: $i] :
( ( relation_dom(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(X0))) = sK15(sK1,sK24(sK1,relation_dom(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95380,c_4468]) ).
tcf(c_95412,plain,
( in(sK24(sK1,relation_rng(sK12)),relation_dom(sK2))
| ( relation_rng(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_95393,c_3810]) ).
tcf(c_95416,plain,
( in(sK24(sK1,relation_rng(sK9)),relation_dom(sK2))
| ( relation_rng(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_95391,c_3808]) ).
tcf(c_95481,plain,
! [X0: $i] :
( in(sK23(relation_rng(X0),sK1),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30448,c_102,c_30448]) ).
tcf(c_95492,plain,
( in(sK23(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_95481]) ).
tcf(c_95494,plain,
( in(sK23(relation_dom(sK9),sK1),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_95481]) ).
tcf(c_95496,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(relation_rng(X0),sK1)) ),
inference(superposition,[status(thm)],[c_95481,c_70]) ).
tcf(c_95497,plain,
! [X0: $i] :
( element(sK23(relation_rng(X0),sK1),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_69]) ).
tcf(c_95500,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(relation_rng(X0),sK1)))) = apply(sK1,sK23(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_12766]) ).
tcf(c_95501,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(relation_rng(X0),sK1)))) = sK7(sK1,sK23(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_12765]) ).
tcf(c_95502,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(relation_rng(X0),sK1)))) = apply(sK1,sK23(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_10203]) ).
tcf(c_95503,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(relation_rng(X0),sK1)))) = sK7(sK1,sK23(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_10202]) ).
tcf(c_95504,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(relation_rng(X0),sK1))) = sK15(sK1,apply(sK1,sK23(relation_rng(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_6249]) ).
tcf(c_95505,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(relation_rng(X0),sK1))) = sK15(sK1,sK7(sK1,sK23(relation_rng(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_5349]) ).
tcf(c_95507,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK23(relation_rng(X0),sK1)) = apply(sK1,sK23(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_12284]) ).
tcf(c_95508,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(relation_rng(X0),sK1))) = sK23(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_4619]) ).
tcf(c_95509,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(relation_rng(X0),sK1))) = sK23(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_4406]) ).
tcf(c_95516,plain,
( in(sK23(relation_dom(sK9),sK1),relation_dom(sK1))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_95494,c_3848]) ).
tcf(c_95520,plain,
( in(sK23(relation_dom(sK12),sK1),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_95492,c_3820]) ).
tcf(c_95555,plain,
! [X0: $i] :
( in(sK24(relation_rng(X0),sK1),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30450,c_102,c_30450]) ).
tcf(c_95566,plain,
( in(sK24(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_95555]) ).
tcf(c_95568,plain,
( in(sK24(relation_dom(sK9),sK1),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_95555]) ).
tcf(c_95570,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(relation_rng(X0),sK1)) ),
inference(superposition,[status(thm)],[c_95555,c_70]) ).
tcf(c_95571,plain,
! [X0: $i] :
( element(sK24(relation_rng(X0),sK1),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_69]) ).
tcf(c_95574,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(relation_rng(X0),sK1))) = apply(sK1,sK15(sK1,sK24(relation_rng(X0),sK1))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_12335]) ).
tcf(c_95575,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(relation_rng(X0),sK1)))) = sK15(sK1,sK24(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_8396]) ).
tcf(c_95576,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(relation_rng(X0),sK1)))) = sK15(sK1,sK24(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_8395]) ).
tcf(c_95577,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK24(relation_rng(X0),sK1))) = sK24(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_4044]) ).
tcf(c_95578,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(relation_rng(X0),sK1)) = apply(sK2,sK24(relation_rng(X0),sK1)) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_95555,c_42224]) ).
tcf(c_95579,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(relation_rng(X0),sK1))) = sK24(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_12701]) ).
tcf(c_95580,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(relation_rng(X0),sK1))) = sK24(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_10144]) ).
tcf(c_95581,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_rng(X0),sK1)) = sK15(sK1,sK24(relation_rng(X0),sK1)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95555,c_4468]) ).
tcf(c_95588,plain,
( in(sK24(relation_dom(sK9),sK1),relation_dom(sK2))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_95568,c_3848]) ).
tcf(c_95592,plain,
( in(sK24(relation_dom(sK12),sK1),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_95566,c_3820]) ).
tcf(c_95754,plain,
! [X0: $i] :
( in(sK23(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30452,c_102,c_30452]) ).
tcf(c_95765,plain,
( in(sK23(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_95754]) ).
tcf(c_95767,plain,
( in(sK23(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_rng(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_95754]) ).
tcf(c_95769,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK1),sK23(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_95754,c_70]) ).
tcf(c_95770,plain,
! [X0: $i] :
( element(sK23(sK1,relation_rng(X0)),relation_dom(sK1))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_69]) ).
tcf(c_95773,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_rng(X0))))) = apply(sK1,sK23(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_12766]) ).
tcf(c_95774,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_rng(X0))))) = sK7(sK1,sK23(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_12765]) ).
tcf(c_95775,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_rng(X0))))) = apply(sK1,sK23(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_10203]) ).
tcf(c_95776,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_rng(X0))))) = sK7(sK1,sK23(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_10202]) ).
tcf(c_95777,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_rng(X0)))) = sK15(sK1,apply(sK1,sK23(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_6249]) ).
tcf(c_95778,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_rng(X0)))) = sK15(sK1,sK7(sK1,sK23(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_5349]) ).
tcf(c_95780,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK23(sK1,relation_rng(X0))) = apply(sK1,sK23(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_12284]) ).
tcf(c_95781,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,relation_rng(X0)))) = sK23(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_4619]) ).
tcf(c_95782,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,relation_rng(X0)))) = sK23(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_4406]) ).
tcf(c_95789,plain,
( in(sK23(sK1,relation_dom(sK9)),relation_dom(sK1))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_95767,c_3848]) ).
tcf(c_95793,plain,
( in(sK23(sK1,relation_dom(sK12)),relation_dom(sK1))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_95765,c_3820]) ).
tcf(c_95828,plain,
! [X0: $i] :
( in(sK24(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(global_subsumption_just,[status(thm)],[c_30454,c_102,c_30454]) ).
tcf(c_95839,plain,
( in(sK24(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK12)) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_95828]) ).
tcf(c_95841,plain,
( in(sK24(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_rng(relation_inverse(sK9)) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_95828]) ).
tcf(c_95843,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ~ empty(X0)
| ~ in(relation_dom(sK2),sK24(sK1,relation_rng(X0))) ),
inference(superposition,[status(thm)],[c_95828,c_70]) ).
tcf(c_95844,plain,
! [X0: $i] :
( element(sK24(sK1,relation_rng(X0)),relation_dom(sK2))
| ( relation_rng(X0) = sK1 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_69]) ).
tcf(c_95847,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,relation_rng(X0)))) = apply(sK1,sK15(sK1,sK24(sK1,relation_rng(X0)))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_12335]) ).
tcf(c_95848,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,relation_rng(X0))))) = sK15(sK1,sK24(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_8396]) ).
tcf(c_95849,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,relation_rng(X0))))) = sK15(sK1,sK24(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_8395]) ).
tcf(c_95850,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK24(sK1,relation_rng(X0)))) = sK24(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_4044]) ).
tcf(c_95851,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,relation_rng(X0))) = apply(sK2,sK24(sK1,relation_rng(X0))) )
| ~ empty(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_95828,c_42224]) ).
tcf(c_95852,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,relation_rng(X0)))) = sK24(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_12701]) ).
tcf(c_95853,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,relation_rng(X0)))) = sK24(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_10144]) ).
tcf(c_95854,plain,
! [X0: $i] :
( ( relation_rng(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_rng(X0))) = sK15(sK1,sK24(sK1,relation_rng(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95828,c_4468]) ).
tcf(c_95861,plain,
( in(sK24(sK1,relation_dom(sK9)),relation_dom(sK2))
| ( relation_dom(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_95841,c_3848]) ).
tcf(c_95865,plain,
( in(sK24(sK1,relation_dom(sK12)),relation_dom(sK2))
| ( relation_dom(sK12) = sK1 )
| ~ empty(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_95839,c_3820]) ).
tcf(c_96025,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35269]) ).
tcf(c_96026,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35269]) ).
tcf(c_96027,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35269]) ).
tcf(c_96028,plain,
relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35269]) ).
tcf(c_96029,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35269]) ).
tcf(c_96030,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35269]) ).
tcf(c_96031,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35269]) ).
tcf(c_96032,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35269]) ).
tcf(c_96033,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35269]) ).
tcf(c_96034,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35269]) ).
tcf(c_96035,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35269]) ).
tcf(c_96036,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35269]) ).
tcf(c_96037,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35269]) ).
tcf(c_96038,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35269]) ).
tcf(c_96039,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35269]) ).
tcf(c_96040,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35269]) ).
tcf(c_96041,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35269]) ).
tcf(c_96160,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35270]) ).
tcf(c_96161,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35270]) ).
tcf(c_96162,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35270]) ).
tcf(c_96163,plain,
relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35270]) ).
tcf(c_96164,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35270]) ).
tcf(c_96165,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35270]) ).
tcf(c_96166,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35270]) ).
tcf(c_96167,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35270]) ).
tcf(c_96168,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35270]) ).
tcf(c_96169,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35270]) ).
tcf(c_96170,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35270]) ).
tcf(c_96171,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35270]) ).
tcf(c_96172,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35270]) ).
tcf(c_96173,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35270]) ).
tcf(c_96174,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35270]) ).
tcf(c_96175,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35270]) ).
tcf(c_96176,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35270]) ).
tcf(c_96355,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35271]) ).
tcf(c_96356,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35271]) ).
tcf(c_96357,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35271]) ).
tcf(c_96358,plain,
relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35271]) ).
tcf(c_96359,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35271]) ).
tcf(c_96360,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35271]) ).
tcf(c_96361,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35271]) ).
tcf(c_96362,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35271]) ).
tcf(c_96363,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35271]) ).
tcf(c_96364,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35271]) ).
tcf(c_96365,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35271]) ).
tcf(c_96366,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35271]) ).
tcf(c_96367,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35271]) ).
tcf(c_96368,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35271]) ).
tcf(c_96369,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35271]) ).
tcf(c_96370,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35271]) ).
tcf(c_96371,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35271]) ).
tcf(c_96409,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35287]) ).
tcf(c_96410,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35287]) ).
tcf(c_96411,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35287]) ).
tcf(c_96412,plain,
relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35287]) ).
tcf(c_96413,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35287]) ).
tcf(c_96414,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35287]) ).
tcf(c_96415,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35287]) ).
tcf(c_96416,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35287]) ).
tcf(c_96417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35287]) ).
tcf(c_96418,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35287]) ).
tcf(c_96419,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35287]) ).
tcf(c_96420,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35287]) ).
tcf(c_96421,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35287]) ).
tcf(c_96422,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35287]) ).
tcf(c_96423,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35287]) ).
tcf(c_96424,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35287]) ).
tcf(c_96425,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35287]) ).
tcf(c_96463,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35288]) ).
tcf(c_96464,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35288]) ).
tcf(c_96465,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35288]) ).
tcf(c_96466,plain,
relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35288]) ).
tcf(c_96467,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35288]) ).
tcf(c_96468,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35288]) ).
tcf(c_96469,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35288]) ).
tcf(c_96470,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35288]) ).
tcf(c_96471,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35288]) ).
tcf(c_96472,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35288]) ).
tcf(c_96473,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35288]) ).
tcf(c_96474,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35288]) ).
tcf(c_96475,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35288]) ).
tcf(c_96476,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35288]) ).
tcf(c_96477,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35288]) ).
tcf(c_96478,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35288]) ).
tcf(c_96479,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35288]) ).
tcf(c_96666,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0) ),
inference(superposition,[status(thm)],[c_34715,c_70]) ).
tcf(c_96667,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_69]) ).
tcf(c_96669,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK5(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_34715,c_76]) ).
tcf(c_96670,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34715,c_106]) ).
tcf(c_96671,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34715,c_78]) ).
tcf(c_96672,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK1),X0) = X1 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34715,c_197]) ).
tcf(c_96674,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK13(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_34715,c_104]) ).
tcf(c_96675,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0) ),
inference(superposition,[status(thm)],[c_34715,c_124]) ).
tcf(c_96676,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_34715,c_129]) ).
tcf(c_96677,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34715,c_12766]) ).
tcf(c_96679,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34715,c_10203]) ).
tcf(c_96680,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34715,c_10202]) ).
tcf(c_96681,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_34715,c_6249]) ).
tcf(c_96682,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_34715,c_5349]) ).
tcf(c_96685,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_34715,c_4619]) ).
tcf(c_96686,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_34715,c_4406]) ).
tcf(c_96688,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_34715,c_13471]) ).
tcf(c_96692,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_10578]) ).
tcf(c_96693,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,X0))) = empty_set )
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_34715,c_12287]) ).
tcf(c_96695,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_92951]) ).
tcf(c_96696,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_89104]) ).
tcf(c_96697,plain,
( ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_dom(sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_9702]) ).
tcf(c_96698,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_34715,c_10491]) ).
tcf(c_96701,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK2,relation_dom(sK1)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_34715,c_43088]) ).
tcf(c_96703,plain,
( ( apply(sK1,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_31455]) ).
tcf(c_96907,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ~ in(relation_dom(sK1),X0) ),
inference(superposition,[status(thm)],[c_34718,c_70]) ).
tcf(c_96908,plain,
! [X0: $i] :
( element(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_69]) ).
tcf(c_96910,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),X1))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK5(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_34718,c_76]) ).
tcf(c_96911,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34718,c_106]) ).
tcf(c_96912,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_dom(sK1)))
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34718,c_78]) ).
tcf(c_96913,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_dom(sK1),X0) = X1 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34718,c_197]) ).
tcf(c_96915,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(X1,sK13(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(relation_dom(sK1))
| ~ in(sK13(relation_dom(sK1),X0),X0) ),
inference(superposition,[status(thm)],[c_34718,c_104]) ).
tcf(c_96916,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0) ),
inference(superposition,[status(thm)],[c_34718,c_124]) ).
tcf(c_96917,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_dom(sK1))
| ~ in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_34718,c_129]) ).
tcf(c_96919,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34718,c_12765]) ).
tcf(c_96920,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34718,c_10203]) ).
tcf(c_96921,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_34718,c_10202]) ).
tcf(c_96922,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = sK15(sK1,apply(sK1,X0)) ) ),
inference(superposition,[status(thm)],[c_34718,c_6249]) ).
tcf(c_96926,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_34718,c_4619]) ).
tcf(c_96929,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_34718,c_13471]) ).
tcf(c_96933,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_10578]) ).
tcf(c_96934,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,X0))) = empty_set )
| ~ in(sK5(sK1,X0),X0) ),
inference(superposition,[status(thm)],[c_34718,c_12287]) ).
tcf(c_96936,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_92951]) ).
tcf(c_96937,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_89104]) ).
tcf(c_96938,plain,
( ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_dom(sK1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_9702]) ).
tcf(c_96939,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))) = empty_set )
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_34718,c_10491]) ).
tcf(c_96942,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK5(sK2,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK2,relation_dom(sK1)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_34718,c_43088]) ).
tcf(c_96944,plain,
( ( apply(sK1,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_dom(sK1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_31455]) ).
tcf(c_97389,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35289]) ).
tcf(c_97390,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35289]) ).
tcf(c_97391,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35289]) ).
tcf(c_97392,plain,
relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35289]) ).
tcf(c_97393,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35289]) ).
tcf(c_97394,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35289]) ).
tcf(c_97395,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35289]) ).
tcf(c_97396,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35289]) ).
tcf(c_97397,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35289]) ).
tcf(c_97398,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35289]) ).
tcf(c_97399,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35289]) ).
tcf(c_97400,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35289]) ).
tcf(c_97401,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35289]) ).
tcf(c_97402,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35289]) ).
tcf(c_97403,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35289]) ).
tcf(c_97404,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35289]) ).
tcf(c_97405,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35289]) ).
tcf(c_97577,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(relation_dom(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_89809]) ).
tcf(c_97578,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(relation_rng(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_89809]) ).
tcf(c_97579,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(relation_inverse(X0))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_89809]) ).
tcf(c_97580,plain,
sK20(sK19(sK19(powerset(empty_set)))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_89809]) ).
tcf(c_97581,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_89809]) ).
tcf(c_97582,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(sK19(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_89809]) ).
tcf(c_97583,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_rng(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_89809]) ).
tcf(c_97584,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_dom(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_89809]) ).
tcf(c_97585,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(sK20(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_89809]) ).
tcf(c_97586,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_rng(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_89809]) ).
tcf(c_97587,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_89809]) ).
tcf(c_97588,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_rng(sK12))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_89809]) ).
tcf(c_97589,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_89809]) ).
tcf(c_97590,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_dom(sK12))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_89809]) ).
tcf(c_97591,plain,
( ( sK20(sK19(sK19(powerset(sK20(powerset(relation_dom(sK9))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_89809]) ).
tcf(c_97592,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(sK20(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_89809]) ).
tcf(c_97593,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(sK19(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_89809]) ).
tcf(c_97626,plain,
( empty(sK19(sK19(powerset(empty_set))))
| ~ in(sK19(sK19(powerset(empty_set))),empty_set) ),
inference(superposition,[status(thm)],[c_97580,c_3486]) ).
tcf(c_97627,plain,
( empty(sK19(sK19(powerset(empty_set))))
| in(empty_set,sK19(sK19(powerset(empty_set)))) ),
inference(superposition,[status(thm)],[c_97580,c_3448]) ).
tcf(c_97628,plain,
element(empty_set,sK19(sK19(powerset(empty_set)))),
inference(superposition,[status(thm)],[c_97580,c_119]) ).
tcf(c_97648,plain,
! [X0: $i] :
( ( sK20(sK19(sK19(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_89809]) ).
tcf(c_97649,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35289]) ).
tcf(c_97650,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35288]) ).
tcf(c_97651,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35287]) ).
tcf(c_97652,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35271]) ).
tcf(c_97653,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35270]) ).
tcf(c_97654,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35269]) ).
tcf(c_97655,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35253]) ).
tcf(c_97656,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35252]) ).
tcf(c_97657,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35251]) ).
tcf(c_97658,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35235]) ).
tcf(c_97659,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35234]) ).
tcf(c_97660,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35233]) ).
tcf(c_97661,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35188]) ).
tcf(c_97662,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35187]) ).
tcf(c_97663,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35186]) ).
tcf(c_97664,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35060]) ).
tcf(c_97665,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35059]) ).
tcf(c_97666,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35058]) ).
tcf(c_97667,plain,
! [X0: $i] :
( ( relation_dom(sK20(sK19(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37371]) ).
tcf(c_97668,plain,
! [X0: $i] :
( ( relation_rng(sK20(sK19(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37370]) ).
tcf(c_97669,plain,
! [X0: $i] :
( ( relation_inverse(sK20(sK19(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37368]) ).
tcf(c_97670,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35042]) ).
tcf(c_97671,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35041]) ).
tcf(c_97672,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35040]) ).
tcf(c_97673,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35024]) ).
tcf(c_97674,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35023]) ).
tcf(c_97675,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35022]) ).
tcf(c_97676,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(sK19(powerset(X0)))))) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = sK14(sK1,sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_6419]) ).
tcf(c_97677,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(sK19(sK19(powerset(X0)))))) = relation_dom(sK1) )
| ( apply(relation_inverse(sK1),sK6(sK1,sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = sK5(sK1,sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_5248]) ).
tcf(c_97678,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29434]) ).
tcf(c_97679,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29433]) ).
tcf(c_97680,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29432]) ).
tcf(c_97681,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29048]) ).
tcf(c_97682,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29047]) ).
tcf(c_97683,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29046]) ).
tcf(c_97684,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29001]) ).
tcf(c_97685,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_29000]) ).
tcf(c_97686,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_28999]) ).
tcf(c_97687,plain,
! [X0: $i,X1: $i] :
( ( sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12147]) ).
tcf(c_97688,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3853]) ).
tcf(c_97689,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3852]) ).
tcf(c_97690,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3847]) ).
tcf(c_97691,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3813]) ).
tcf(c_97692,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3812]) ).
tcf(c_97693,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3807]) ).
tcf(c_97694,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_39387]) ).
tcf(c_97695,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_39386]) ).
tcf(c_97696,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_39385]) ).
tcf(c_97697,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34275]) ).
tcf(c_97698,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34274]) ).
tcf(c_97699,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34273]) ).
tcf(c_97700,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34257]) ).
tcf(c_97701,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34256]) ).
tcf(c_97702,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_34255]) ).
tcf(c_97703,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_27401]) ).
tcf(c_97704,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_27400]) ).
tcf(c_97705,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_27399]) ).
tcf(c_97706,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25347]) ).
tcf(c_97707,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25346]) ).
tcf(c_97708,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25345]) ).
tcf(c_97709,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25312]) ).
tcf(c_97710,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25311]) ).
tcf(c_97711,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25310]) ).
tcf(c_97712,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25248]) ).
tcf(c_97713,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25247]) ).
tcf(c_97714,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25246]) ).
tcf(c_97715,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24512]) ).
tcf(c_97716,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24511]) ).
tcf(c_97717,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24510]) ).
tcf(c_97718,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24398]) ).
tcf(c_97719,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24397]) ).
tcf(c_97720,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24396]) ).
tcf(c_97721,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24361]) ).
tcf(c_97722,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24360]) ).
tcf(c_97723,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24359]) ).
tcf(c_97724,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24299]) ).
tcf(c_97725,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24298]) ).
tcf(c_97726,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24297]) ).
tcf(c_97727,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23557]) ).
tcf(c_97728,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23556]) ).
tcf(c_97729,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23555]) ).
tcf(c_97730,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23520]) ).
tcf(c_97731,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23519]) ).
tcf(c_97732,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23518]) ).
tcf(c_97733,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23406]) ).
tcf(c_97734,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23405]) ).
tcf(c_97735,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23404]) ).
tcf(c_97736,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23371]) ).
tcf(c_97737,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23370]) ).
tcf(c_97738,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23369]) ).
tcf(c_97739,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_22305]) ).
tcf(c_97740,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_22304]) ).
tcf(c_97741,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_22303]) ).
tcf(c_97742,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_21079]) ).
tcf(c_97743,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_21078]) ).
tcf(c_97744,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_21077]) ).
tcf(c_97745,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20790]) ).
tcf(c_97746,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20789]) ).
tcf(c_97747,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20788]) ).
tcf(c_97748,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20733]) ).
tcf(c_97749,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20732]) ).
tcf(c_97750,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20731]) ).
tcf(c_97751,plain,
! [X0: $i] :
( ( sK20(powerset(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14787]) ).
tcf(c_97752,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20567]) ).
tcf(c_97753,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20566]) ).
tcf(c_97754,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20565]) ).
tcf(c_97755,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19623]) ).
tcf(c_97756,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14242]) ).
tcf(c_97757,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14162]) ).
tcf(c_97758,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14077]) ).
tcf(c_97759,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12144]) ).
tcf(c_97760,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19622]) ).
tcf(c_97761,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19621]) ).
tcf(c_97762,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12143]) ).
tcf(c_97763,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12142]) ).
tcf(c_97764,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12141]) ).
tcf(c_97765,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12140]) ).
tcf(c_97766,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19044]) ).
tcf(c_97767,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19043]) ).
tcf(c_97768,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12139]) ).
tcf(c_97769,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19042]) ).
tcf(c_97770,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18986]) ).
tcf(c_97771,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18985]) ).
tcf(c_97772,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18984]) ).
tcf(c_97773,plain,
! [X0: $i] :
( ( sK20(sK19(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_36589]) ).
tcf(c_97774,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18933]) ).
tcf(c_97775,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18932]) ).
tcf(c_97776,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18931]) ).
tcf(c_97777,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18887]) ).
tcf(c_97778,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18886]) ).
tcf(c_97779,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18885]) ).
tcf(c_97780,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18057]) ).
tcf(c_97781,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18056]) ).
tcf(c_97782,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18055]) ).
tcf(c_97783,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17694]) ).
tcf(c_97784,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17693]) ).
tcf(c_97785,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17692]) ).
tcf(c_97786,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17624]) ).
tcf(c_97787,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17623]) ).
tcf(c_97788,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17622]) ).
tcf(c_97789,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17580]) ).
tcf(c_97790,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17579]) ).
tcf(c_97791,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17578]) ).
tcf(c_97792,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17545]) ).
tcf(c_97793,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17544]) ).
tcf(c_97794,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17543]) ).
tcf(c_97795,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_16055]) ).
tcf(c_97796,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_16054]) ).
tcf(c_97797,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_16053]) ).
tcf(c_97798,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15952]) ).
tcf(c_97799,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15951]) ).
tcf(c_97800,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15950]) ).
tcf(c_97801,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15917]) ).
tcf(c_97802,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15916]) ).
tcf(c_97803,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15915]) ).
tcf(c_97804,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15880]) ).
tcf(c_97805,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15879]) ).
tcf(c_97806,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15878]) ).
tcf(c_97807,plain,
! [X0: $i] :
( ( relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12149]) ).
tcf(c_97808,plain,
! [X0: $i] :
( ( relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12148]) ).
tcf(c_97809,plain,
! [X0: $i] :
( ( function_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11026]) ).
tcf(c_97810,plain,
! [X0: $i] :
( ( function_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11025]) ).
tcf(c_97811,plain,
! [X0: $i] :
( ( function_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11024]) ).
tcf(c_97812,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3663]) ).
tcf(c_97813,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3662]) ).
tcf(c_97814,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3661]) ).
tcf(c_97815,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3632]) ).
tcf(c_97816,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_12146]) ).
tcf(c_97817,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3631]) ).
tcf(c_97818,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_3626]) ).
tcf(c_97819,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14780]) ).
tcf(c_97820,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14779]) ).
tcf(c_97821,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14778]) ).
tcf(c_97822,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14235]) ).
tcf(c_97823,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14234]) ).
tcf(c_97824,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14233]) ).
tcf(c_97825,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14155]) ).
tcf(c_97826,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14154]) ).
tcf(c_97827,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14153]) ).
tcf(c_97828,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14070]) ).
tcf(c_97829,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14069]) ).
tcf(c_97830,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_14068]) ).
tcf(c_97831,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11811]) ).
tcf(c_97832,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11810]) ).
tcf(c_97833,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11809]) ).
tcf(c_97834,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11771]) ).
tcf(c_97835,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11770]) ).
tcf(c_97836,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11769]) ).
tcf(c_97837,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11729]) ).
tcf(c_97838,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11728]) ).
tcf(c_97839,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11727]) ).
tcf(c_97840,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11691]) ).
tcf(c_97841,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11690]) ).
tcf(c_97842,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11689]) ).
tcf(c_97843,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11660]) ).
tcf(c_97844,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11659]) ).
tcf(c_97845,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11658]) ).
tcf(c_97846,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11297]) ).
tcf(c_97847,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11296]) ).
tcf(c_97848,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_11295]) ).
tcf(c_97859,plain,
! [X0: $i] :
( ( function_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) = relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_957]) ).
tcf(c_97865,plain,
! [X0: $i] :
( relation(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_94]) ).
tcf(c_97866,plain,
! [X0: $i] :
( function(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_85]) ).
tcf(c_99008,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_38530]) ).
tcf(c_99009,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_38530]) ).
tcf(c_99010,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_38530]) ).
tcf(c_99011,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_38530]) ).
tcf(c_99012,plain,
( ( apply(sK2,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_38530]) ).
tcf(c_99013,plain,
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_38530]) ).
tcf(c_99015,plain,
( ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_dom(sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_38530]) ).
tcf(c_99052,plain,
apply(sK2,relation_dom(sK2)) = empty_set,
inference(global_subsumption_just,[status(thm)],[c_99013,c_70910,c_71015,c_92924]) ).
tcf(c_99061,plain,
( ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99052,c_19430]) ).
tcf(c_99062,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99052,c_4045]) ).
tcf(c_99063,plain,
( element(empty_set,relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99052,c_19431]) ).
tcf(c_99064,plain,
( in(empty_set,relation_rng(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99052,c_18734]) ).
tcf(c_99065,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99052,c_87]) ).
tcf(c_99077,plain,
( in(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99065,c_62,c_61]) ).
tcf(c_99095,plain,
( ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ in(sK2,ordered_pair(relation_dom(sK2),empty_set)) ),
inference(superposition,[status(thm)],[c_99077,c_70]) ).
tcf(c_99096,plain,
( element(ordered_pair(relation_dom(sK2),empty_set),sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99077,c_69]) ).
tcf(c_99098,plain,
( in(empty_set,relation_rng(sK2))
| ~ relation(sK2)
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99077,c_106]) ).
tcf(c_99105,plain,
( in(empty_set,relation_rng(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99098,c_61]) ).
tcf(c_99180,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_97865,c_72]) ).
tcf(c_99181,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_97865,c_71]) ).
tcf(c_99182,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0)))))))) = sK20(powerset(sK20(sK19(sK19(powerset(X0)))))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_97865,c_120]) ).
tcf(c_99198,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35571]) ).
tcf(c_99199,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35571]) ).
tcf(c_99200,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35571]) ).
tcf(c_99201,plain,
relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35571]) ).
tcf(c_99202,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35571]) ).
tcf(c_99203,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35571]) ).
tcf(c_99204,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35571]) ).
tcf(c_99205,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35571]) ).
tcf(c_99206,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35571]) ).
tcf(c_99207,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35571]) ).
tcf(c_99208,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35571]) ).
tcf(c_99209,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35571]) ).
tcf(c_99210,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35571]) ).
tcf(c_99211,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35571]) ).
tcf(c_99212,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35571]) ).
tcf(c_99213,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35571]) ).
tcf(c_99214,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35571]) ).
tcf(c_99215,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35571]) ).
tcf(c_99399,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35572]) ).
tcf(c_99400,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35572]) ).
tcf(c_99401,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35572]) ).
tcf(c_99402,plain,
relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35572]) ).
tcf(c_99403,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35572]) ).
tcf(c_99404,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35572]) ).
tcf(c_99405,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35572]) ).
tcf(c_99406,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35572]) ).
tcf(c_99407,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35572]) ).
tcf(c_99408,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35572]) ).
tcf(c_99409,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35572]) ).
tcf(c_99410,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35572]) ).
tcf(c_99411,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35572]) ).
tcf(c_99412,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35572]) ).
tcf(c_99413,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35572]) ).
tcf(c_99414,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35572]) ).
tcf(c_99415,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35572]) ).
tcf(c_99416,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35572]) ).
tcf(c_99536,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35573]) ).
tcf(c_99537,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35573]) ).
tcf(c_99538,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35573]) ).
tcf(c_99539,plain,
relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35573]) ).
tcf(c_99540,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35573]) ).
tcf(c_99541,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35573]) ).
tcf(c_99542,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35573]) ).
tcf(c_99543,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35573]) ).
tcf(c_99544,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35573]) ).
tcf(c_99545,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35573]) ).
tcf(c_99546,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35573]) ).
tcf(c_99547,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35573]) ).
tcf(c_99548,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35573]) ).
tcf(c_99549,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35573]) ).
tcf(c_99550,plain,
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35573]) ).
tcf(c_99551,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35573]) ).
tcf(c_99552,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35573]) ).
tcf(c_99553,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35573]) ).
tcf(c_99593,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35610]) ).
tcf(c_99594,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35610]) ).
tcf(c_99595,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35610]) ).
tcf(c_99596,plain,
relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35610]) ).
tcf(c_99597,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35610]) ).
tcf(c_99598,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35610]) ).
tcf(c_99599,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35610]) ).
tcf(c_99600,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35610]) ).
tcf(c_99601,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35610]) ).
tcf(c_99602,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35610]) ).
tcf(c_99603,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35610]) ).
tcf(c_99604,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35610]) ).
tcf(c_99605,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35610]) ).
tcf(c_99606,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35610]) ).
tcf(c_99607,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35610]) ).
tcf(c_99608,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35610]) ).
tcf(c_99609,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35610]) ).
tcf(c_99610,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35610]) ).
tcf(c_100030,plain,
! [X0: $i] :
( ( apply(sK1,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_56485]) ).
tcf(c_100034,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_56485]) ).
tcf(c_100037,plain,
( ( apply(sK1,relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_56485]) ).
tcf(c_100061,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_64169,c_100034]) ).
tcf(c_100067,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100034,c_19430]) ).
tcf(c_100068,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100034,c_4045]) ).
tcf(c_100069,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100034,c_19431]) ).
tcf(c_100070,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100034,c_18734]) ).
tcf(c_100071,plain,
( in(ordered_pair(sK7(sK1,relation_dom(sK1)),empty_set),sK2)
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100034,c_87]) ).
tcf(c_100089,plain,
( in(ordered_pair(sK7(sK1,relation_dom(sK1)),empty_set),sK2)
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100071,c_62,c_61]) ).
tcf(c_100110,plain,
( in(ordered_pair(apply(sK1,relation_dom(sK1)),empty_set),sK2)
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64169,c_100089]) ).
tcf(c_100111,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2))
| ~ in(sK2,ordered_pair(sK7(sK1,relation_dom(sK1)),empty_set)) ),
inference(superposition,[status(thm)],[c_100089,c_70]) ).
tcf(c_100112,plain,
( element(ordered_pair(sK7(sK1,relation_dom(sK1)),empty_set),sK2)
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100089,c_69]) ).
tcf(c_100114,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ relation(sK2)
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_100089,c_106]) ).
tcf(c_100119,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100114,c_61]) ).
tcf(c_100140,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_100119]) ).
tcf(c_100141,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(relation_dom(sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_100119]) ).
tcf(c_100142,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(apply(sK1,relation_dom(sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64169,c_100119]) ).
tcf(c_100158,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_100141]) ).
tcf(c_100163,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100158,c_65,c_64]) ).
tcf(c_100173,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(relation_rng(sK2),empty_set) ),
inference(superposition,[status(thm)],[c_100163,c_70]) ).
tcf(c_100174,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_100163,c_69]) ).
tcf(c_100176,plain,
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),empty_set)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_100163,c_43161]) ).
tcf(c_100193,plain,
! [X0: $i] :
( ( apply(sK1,relation_dom(X0)) = empty_set )
| ( apply(X0,relation_dom(sK1)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_58008]) ).
tcf(c_100200,plain,
( ( apply(sK1,relation_rng(sK2)) = empty_set )
| ( apply(relation_inverse(sK2),relation_dom(sK1)) = empty_set )
| ( apply(sK2,apply(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_58008]) ).
tcf(c_100224,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35611]) ).
tcf(c_100225,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35611]) ).
tcf(c_100226,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35611]) ).
tcf(c_100227,plain,
relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35611]) ).
tcf(c_100228,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35611]) ).
tcf(c_100229,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35611]) ).
tcf(c_100230,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35611]) ).
tcf(c_100231,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35611]) ).
tcf(c_100232,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35611]) ).
tcf(c_100233,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35611]) ).
tcf(c_100234,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35611]) ).
tcf(c_100235,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35611]) ).
tcf(c_100236,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35611]) ).
tcf(c_100237,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35611]) ).
tcf(c_100238,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35611]) ).
tcf(c_100239,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35611]) ).
tcf(c_100240,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35611]) ).
tcf(c_100241,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35611]) ).
tcf(c_100335,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35612]) ).
tcf(c_100336,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35612]) ).
tcf(c_100337,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35612]) ).
tcf(c_100338,plain,
relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35612]) ).
tcf(c_100339,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35612]) ).
tcf(c_100340,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35612]) ).
tcf(c_100341,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35612]) ).
tcf(c_100342,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35612]) ).
tcf(c_100343,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35612]) ).
tcf(c_100344,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35612]) ).
tcf(c_100345,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35612]) ).
tcf(c_100346,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35612]) ).
tcf(c_100347,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35612]) ).
tcf(c_100348,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35612]) ).
tcf(c_100349,plain,
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35612]) ).
tcf(c_100350,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35612]) ).
tcf(c_100351,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35612]) ).
tcf(c_100352,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35612]) ).
tcf(c_100392,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35628]) ).
tcf(c_100393,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35628]) ).
tcf(c_100394,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35628]) ).
tcf(c_100395,plain,
relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35628]) ).
tcf(c_100396,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35628]) ).
tcf(c_100397,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35628]) ).
tcf(c_100398,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35628]) ).
tcf(c_100399,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35628]) ).
tcf(c_100400,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35628]) ).
tcf(c_100401,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35628]) ).
tcf(c_100402,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35628]) ).
tcf(c_100403,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35628]) ).
tcf(c_100404,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35628]) ).
tcf(c_100405,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35628]) ).
tcf(c_100406,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35628]) ).
tcf(c_100407,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35628]) ).
tcf(c_100408,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35628]) ).
tcf(c_100409,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35628]) ).
tcf(c_100533,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_52427,c_64920]) ).
tcf(c_100534,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_8695,c_64920]) ).
tcf(c_100537,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,apply(relation_inverse(sK1),empty_set)) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_64920]) ).
tcf(c_100538,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_10201,c_64920]) ).
tcf(c_100539,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_10244,c_64920]) ).
tcf(c_100541,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_60275,c_64920]) ).
tcf(c_100542,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_61136,c_64920]) ).
tcf(c_100543,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_10207,c_64920]) ).
tcf(c_100544,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_10226,c_64920]) ).
tcf(c_100545,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_10228,c_64920]) ).
tcf(c_100547,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_10231,c_64920]) ).
tcf(c_100548,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_13385,c_64920]) ).
tcf(c_100549,plain,
( ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_14032,c_64920]) ).
tcf(c_100557,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_64168,c_64920]) ).
tcf(c_100563,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_87]) ).
tcf(c_100564,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),apply(relation_inverse(sK1),apply(sK1,X0))),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_12604]) ).
tcf(c_100565,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_12599]) ).
tcf(c_100566,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_61586]) ).
tcf(c_100568,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64920,c_57811]) ).
tcf(c_100574,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(relation_dom(sK2),apply(sK1,X0))
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_6246]) ).
tcf(c_100575,plain,
! [X0: $i] :
( element(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_6247]) ).
tcf(c_100576,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_5332]) ).
tcf(c_100631,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100563,c_65,c_64]) ).
tcf(c_100756,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56725,c_100631]) ).
tcf(c_100757,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4791,c_100631]) ).
tcf(c_100759,plain,
( in(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_6420,c_100631]) ).
tcf(c_100760,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),apply(sK1,sK15(sK1,X0))),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_58270,c_100631]) ).
tcf(c_100761,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8770,c_100631]) ).
tcf(c_100762,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8797,c_100631]) ).
tcf(c_100763,plain,
( in(ordered_pair(sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK14(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10032,c_100631]) ).
tcf(c_100803,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(sK2,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_52427,c_100631]) ).
tcf(c_100804,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(sK2,sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8695,c_100631]) ).
tcf(c_100805,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12791,c_100631]) ).
tcf(c_100806,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13464,c_100631]) ).
tcf(c_100810,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10244,c_100631]) ).
tcf(c_100812,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_60275,c_100631]) ).
tcf(c_100813,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61136,c_100631]) ).
tcf(c_100814,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10207,c_100631]) ).
tcf(c_100815,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10226,c_100631]) ).
tcf(c_100816,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10228,c_100631]) ).
tcf(c_100818,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_10231,c_100631]) ).
tcf(c_100820,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12807,c_100631]) ).
tcf(c_100821,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_63810,c_100631]) ).
tcf(c_100822,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64920,c_100631]) ).
tcf(c_100823,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12770,c_100631]) ).
tcf(c_100824,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12789,c_100631]) ).
tcf(c_100825,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12794,c_100631]) ).
tcf(c_100826,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13383,c_100631]) ).
tcf(c_100827,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_13385,c_100631]) ).
tcf(c_100828,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14030,c_100631]) ).
tcf(c_100829,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14032,c_100631]) ).
tcf(c_100837,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK7(sK1,X0)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_64168,c_100631]) ).
tcf(c_100840,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_100631,c_70]) ).
tcf(c_100841,plain,
! [X0: $i] :
( element(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_100631,c_69]) ).
tcf(c_100843,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_100631,c_106]) ).
tcf(c_100852,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100843,c_4013]) ).
tcf(c_101291,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK24(sK1,relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_72747,c_70]) ).
tcf(c_101292,plain,
( element(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_72747,c_69]) ).
tcf(c_101295,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,relation_inverse(sK1)))) = apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1)))) ) ),
inference(superposition,[status(thm)],[c_72747,c_12335]) ).
tcf(c_101296,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1))))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_72747,c_8396]) ).
tcf(c_101297,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1))))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_72747,c_8395]) ).
tcf(c_101298,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_72747,c_4044]) ).
tcf(c_101299,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,relation_inverse(sK1))) = apply(sK2,sK24(sK1,relation_inverse(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_72747,c_42224]) ).
tcf(c_101300,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_72747,c_12701]) ).
tcf(c_101301,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_72747,c_10144]) ).
tcf(c_101302,plain,
( in(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_72747,c_4468]) ).
tcf(c_101341,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK24(sK1,relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_75654,c_70]) ).
tcf(c_101342,plain,
( element(sK24(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_75654,c_69]) ).
tcf(c_101345,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,relation_inverse(sK1)))) = apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1)))) ) ),
inference(superposition,[status(thm)],[c_75654,c_12335]) ).
tcf(c_101346,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1))))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_75654,c_8396]) ).
tcf(c_101347,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,relation_inverse(sK1))))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_75654,c_8395]) ).
tcf(c_101348,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_75654,c_4044]) ).
tcf(c_101349,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(sK1,relation_inverse(sK1))) = apply(sK2,sK24(sK1,relation_inverse(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_75654,c_42224]) ).
tcf(c_101350,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_75654,c_12701]) ).
tcf(c_101351,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_75654,c_10144]) ).
tcf(c_101352,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1))) = sK15(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_75654,c_4468]) ).
tcf(c_101391,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK24(relation_inverse(sK1),sK1)) ),
inference(superposition,[status(thm)],[c_80729,c_70]) ).
tcf(c_101392,plain,
( element(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_80729,c_69]) ).
tcf(c_101395,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(relation_inverse(sK1),sK1))) = apply(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1))) ) ),
inference(superposition,[status(thm)],[c_80729,c_12335]) ).
tcf(c_101396,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1)))) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80729,c_8396]) ).
tcf(c_101397,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1)))) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80729,c_8395]) ).
tcf(c_101398,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80729,c_4044]) ).
tcf(c_101399,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(relation_inverse(sK1),sK1)) = apply(sK2,sK24(relation_inverse(sK1),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80729,c_42224]) ).
tcf(c_101400,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80729,c_12701]) ).
tcf(c_101401,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80729,c_10144]) ).
tcf(c_101402,plain,
( in(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1)) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80729,c_4468]) ).
tcf(c_101441,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK24(relation_inverse(sK1),sK1)) ),
inference(superposition,[status(thm)],[c_80940,c_70]) ).
tcf(c_101442,plain,
( element(sK24(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_80940,c_69]) ).
tcf(c_101445,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK24(relation_inverse(sK1),sK1))) = apply(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1))) ) ),
inference(superposition,[status(thm)],[c_80940,c_12335]) ).
tcf(c_101446,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1)))) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80940,c_8396]) ).
tcf(c_101447,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(relation_inverse(sK1),sK1)))) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80940,c_8395]) ).
tcf(c_101448,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80940,c_4044]) ).
tcf(c_101449,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK24(relation_inverse(sK1),sK1)) = apply(sK2,sK24(relation_inverse(sK1),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_80940,c_42224]) ).
tcf(c_101450,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80940,c_12701]) ).
tcf(c_101451,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_80940,c_10144]) ).
tcf(c_101452,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1)) = sK15(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_80940,c_4468]) ).
tcf(c_101648,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK1),sK24(sK1,relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_85387,c_70]) ).
tcf(c_101649,plain,
( element(sK24(sK1,relation_inverse(sK1)),relation_dom(sK1))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_85387,c_69]) ).
tcf(c_101652,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK24(sK1,relation_inverse(sK1))))) = apply(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85387,c_12766]) ).
tcf(c_101653,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK24(sK1,relation_inverse(sK1))))) = sK7(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85387,c_12765]) ).
tcf(c_101654,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK24(sK1,relation_inverse(sK1))))) = apply(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85387,c_10203]) ).
tcf(c_101655,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK24(sK1,relation_inverse(sK1))))) = sK7(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85387,c_10202]) ).
tcf(c_101656,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK24(sK1,relation_inverse(sK1)))) = sK15(sK1,apply(sK1,sK24(sK1,relation_inverse(sK1)))) ) ),
inference(superposition,[status(thm)],[c_85387,c_6249]) ).
tcf(c_101657,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK24(sK1,relation_inverse(sK1)))) = sK15(sK1,sK7(sK1,sK24(sK1,relation_inverse(sK1)))) ) ),
inference(superposition,[status(thm)],[c_85387,c_5349]) ).
tcf(c_101659,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK24(sK1,relation_inverse(sK1))) = apply(sK1,sK24(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85387,c_12284]) ).
tcf(c_101660,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85387,c_4619]) ).
tcf(c_101661,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85387,c_4406]) ).
tcf(c_101710,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35629]) ).
tcf(c_101711,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35629]) ).
tcf(c_101712,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35629]) ).
tcf(c_101713,plain,
relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35629]) ).
tcf(c_101714,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35629]) ).
tcf(c_101715,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35629]) ).
tcf(c_101716,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35629]) ).
tcf(c_101717,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35629]) ).
tcf(c_101718,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35629]) ).
tcf(c_101719,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35629]) ).
tcf(c_101720,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35629]) ).
tcf(c_101721,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35629]) ).
tcf(c_101722,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35629]) ).
tcf(c_101723,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35629]) ).
tcf(c_101724,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35629]) ).
tcf(c_101725,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35629]) ).
tcf(c_101726,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35629]) ).
tcf(c_101727,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35629]) ).
tcf(c_101767,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35630]) ).
tcf(c_101768,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35630]) ).
tcf(c_101769,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35630]) ).
tcf(c_101770,plain,
relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35630]) ).
tcf(c_101771,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35630]) ).
tcf(c_101772,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35630]) ).
tcf(c_101773,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35630]) ).
tcf(c_101774,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35630]) ).
tcf(c_101775,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35630]) ).
tcf(c_101776,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35630]) ).
tcf(c_101777,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35630]) ).
tcf(c_101778,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35630]) ).
tcf(c_101779,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35630]) ).
tcf(c_101780,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35630]) ).
tcf(c_101781,plain,
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35630]) ).
tcf(c_101782,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35630]) ).
tcf(c_101783,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35630]) ).
tcf(c_101784,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35630]) ).
tcf(c_101891,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35646]) ).
tcf(c_101892,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35646]) ).
tcf(c_101893,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35646]) ).
tcf(c_101894,plain,
relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35646]) ).
tcf(c_101895,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35646]) ).
tcf(c_101896,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35646]) ).
tcf(c_101897,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35646]) ).
tcf(c_101898,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35646]) ).
tcf(c_101899,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35646]) ).
tcf(c_101900,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35646]) ).
tcf(c_101901,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35646]) ).
tcf(c_101902,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35646]) ).
tcf(c_101903,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35646]) ).
tcf(c_101904,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35646]) ).
tcf(c_101905,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35646]) ).
tcf(c_101906,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35646]) ).
tcf(c_101907,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35646]) ).
tcf(c_101908,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35646]) ).
tcf(c_101991,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35647]) ).
tcf(c_101992,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35647]) ).
tcf(c_101993,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35647]) ).
tcf(c_101994,plain,
relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35647]) ).
tcf(c_101995,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35647]) ).
tcf(c_101996,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35647]) ).
tcf(c_101997,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35647]) ).
tcf(c_101998,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35647]) ).
tcf(c_101999,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35647]) ).
tcf(c_102000,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35647]) ).
tcf(c_102001,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35647]) ).
tcf(c_102002,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35647]) ).
tcf(c_102003,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35647]) ).
tcf(c_102004,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35647]) ).
tcf(c_102005,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35647]) ).
tcf(c_102006,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35647]) ).
tcf(c_102007,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35647]) ).
tcf(c_102008,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35647]) ).
tcf(c_102205,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK23(sK1,relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_85545,c_70]) ).
tcf(c_102206,plain,
( element(sK23(sK1,relation_inverse(sK1)),relation_dom(sK2))
| in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_85545,c_69]) ).
tcf(c_102209,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,relation_inverse(sK1)))) = apply(sK1,sK15(sK1,sK23(sK1,relation_inverse(sK1)))) ) ),
inference(superposition,[status(thm)],[c_85545,c_12335]) ).
tcf(c_102210,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,relation_inverse(sK1))))) = sK15(sK1,sK23(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85545,c_8396]) ).
tcf(c_102211,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,relation_inverse(sK1))))) = sK15(sK1,sK23(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85545,c_8395]) ).
tcf(c_102212,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK23(sK1,relation_inverse(sK1)))) = sK23(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85545,c_4044]) ).
tcf(c_102213,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK23(sK1,relation_inverse(sK1))) = apply(sK2,sK23(sK1,relation_inverse(sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_85545,c_42224]) ).
tcf(c_102214,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,relation_inverse(sK1)))) = sK23(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85545,c_12701]) ).
tcf(c_102215,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,relation_inverse(sK1)))) = sK23(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85545,c_10144]) ).
tcf(c_102216,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK23(sK1,relation_inverse(sK1))) = sK15(sK1,sK23(sK1,relation_inverse(sK1))) ) ),
inference(superposition,[status(thm)],[c_85545,c_4468]) ).
tcf(c_102288,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK1),sK24(relation_inverse(sK1),sK1)) ),
inference(superposition,[status(thm)],[c_86834,c_70]) ).
tcf(c_102289,plain,
( element(sK24(relation_inverse(sK1),sK1),relation_dom(sK1))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_86834,c_69]) ).
tcf(c_102292,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK24(relation_inverse(sK1),sK1)))) = apply(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86834,c_12766]) ).
tcf(c_102293,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK24(relation_inverse(sK1),sK1)))) = sK7(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86834,c_12765]) ).
tcf(c_102294,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK24(relation_inverse(sK1),sK1)))) = apply(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86834,c_10203]) ).
tcf(c_102295,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK24(relation_inverse(sK1),sK1)))) = sK7(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86834,c_10202]) ).
tcf(c_102296,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK24(relation_inverse(sK1),sK1))) = sK15(sK1,apply(sK1,sK24(relation_inverse(sK1),sK1))) ) ),
inference(superposition,[status(thm)],[c_86834,c_6249]) ).
tcf(c_102297,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK24(relation_inverse(sK1),sK1))) = sK15(sK1,sK7(sK1,sK24(relation_inverse(sK1),sK1))) ) ),
inference(superposition,[status(thm)],[c_86834,c_5349]) ).
tcf(c_102299,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK24(relation_inverse(sK1),sK1)) = apply(sK1,sK24(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86834,c_12284]) ).
tcf(c_102300,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86834,c_4619]) ).
tcf(c_102301,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86834,c_4406]) ).
tcf(c_102345,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ~ in(relation_dom(sK2),sK23(relation_inverse(sK1),sK1)) ),
inference(superposition,[status(thm)],[c_86934,c_70]) ).
tcf(c_102346,plain,
( element(sK23(relation_inverse(sK1),sK1),relation_dom(sK2))
| in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 ) ),
inference(superposition,[status(thm)],[c_86934,c_69]) ).
tcf(c_102349,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(relation_inverse(sK1),sK1))) = apply(sK1,sK15(sK1,sK23(relation_inverse(sK1),sK1))) ) ),
inference(superposition,[status(thm)],[c_86934,c_12335]) ).
tcf(c_102350,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(relation_inverse(sK1),sK1)))) = sK15(sK1,sK23(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86934,c_8396]) ).
tcf(c_102351,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(relation_inverse(sK1),sK1)))) = sK15(sK1,sK23(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86934,c_8395]) ).
tcf(c_102352,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK23(relation_inverse(sK1),sK1))) = sK23(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86934,c_4044]) ).
tcf(c_102353,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK23(relation_inverse(sK1),sK1)) = apply(sK2,sK23(relation_inverse(sK1),sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_86934,c_42224]) ).
tcf(c_102354,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(relation_inverse(sK1),sK1))) = sK23(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86934,c_12701]) ).
tcf(c_102355,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(relation_inverse(sK1),sK1))) = sK23(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86934,c_10144]) ).
tcf(c_102356,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK23(relation_inverse(sK1),sK1)) = sK15(sK1,sK23(relation_inverse(sK1),sK1)) ) ),
inference(superposition,[status(thm)],[c_86934,c_4468]) ).
tcf(c_102468,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK12))
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_6672]) ).
tcf(c_102469,plain,
( in(sK21(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_6672]) ).
tcf(c_102470,plain,
( in(sK21(sK1,relation_inverse(sK9)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK9)),relation_dom(sK9))
| ( relation_inverse(sK1) = relation_inverse(sK9) )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_6672]) ).
tcf(c_102471,plain,
( in(sK21(sK1,relation_inverse(sK10)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK10)),relation_dom(sK10))
| ( relation_inverse(sK1) = relation_inverse(sK10) )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_6672]) ).
tcf(c_102472,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_dom(sK2),sK21(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6672,c_70]) ).
tcf(c_102473,plain,
! [X0: $i] :
( element(sK21(sK1,X0),relation_dom(sK2))
| in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_69]) ).
tcf(c_102476,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,X0))) = apply(sK1,sK15(sK1,sK21(sK1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_12335]) ).
tcf(c_102477,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_8396]) ).
tcf(c_102478,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_8395]) ).
tcf(c_102479,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_4044]) ).
tcf(c_102480,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK21(sK1,X0)) = apply(sK2,sK21(sK1,X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6672,c_42224]) ).
tcf(c_102481,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_12701]) ).
tcf(c_102482,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_10144]) ).
tcf(c_102483,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_4468]) ).
tcf(c_102485,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK22(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6672,c_70]) ).
tcf(c_102486,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| element(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6672,c_69]) ).
tcf(c_102487,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6672,c_67]) ).
tcf(c_102488,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,sK2))) = sK22(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6672,c_43161]) ).
tcf(c_102489,plain,
( in(sK21(sK1,sK9),relation_dom(sK2))
| ( relation_inverse(sK1) = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_6672,c_29938]) ).
tcf(c_102490,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_6672,c_69454]) ).
tcf(c_102492,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102490,c_95]) ).
tcf(c_102496,plain,
( in(sK21(sK1,sK9),relation_dom(sK2))
| ( relation_inverse(sK1) = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102489,c_83]) ).
tcf(c_102532,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK12))
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102468,c_3610]) ).
tcf(c_102548,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,sK2))) = sK22(sK1,sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102488,c_61]) ).
tcf(c_102662,plain,
( in(sK21(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(sK21(sK1,relation_inverse(sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_6673]) ).
tcf(c_102663,plain,
( in(sK21(sK1,relation_inverse(sK9)),relation_dom(sK2))
| in(sK21(sK1,relation_inverse(sK9)),relation_rng(sK9))
| ( relation_inverse(sK1) = relation_inverse(sK9) )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_6673]) ).
tcf(c_102664,plain,
( in(sK21(sK1,relation_inverse(sK10)),relation_dom(sK2))
| in(sK21(sK1,relation_inverse(sK10)),relation_rng(sK10))
| ( relation_inverse(sK1) = relation_inverse(sK10) )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_6673]) ).
tcf(c_102665,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK21(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_6673]) ).
tcf(c_102666,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_dom(sK2),sK21(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6673,c_70]) ).
tcf(c_102667,plain,
! [X0: $i] :
( element(sK21(sK1,X0),relation_dom(sK2))
| in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_69]) ).
tcf(c_102670,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,X0))) = apply(sK1,sK15(sK1,sK21(sK1,X0))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_12335]) ).
tcf(c_102671,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_8396]) ).
tcf(c_102672,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,X0)))) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_8395]) ).
tcf(c_102673,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(sK2,sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_4044]) ).
tcf(c_102674,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( sK15(relation_inverse(sK2),sK21(sK1,X0)) = apply(sK2,sK21(sK1,X0)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_6673,c_42224]) ).
tcf(c_102675,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_12701]) ).
tcf(c_102676,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,X0))) = sK21(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_10144]) ).
tcf(c_102677,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ( apply(relation_inverse(sK1),sK21(sK1,X0)) = sK15(sK1,sK21(sK1,X0)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_4468]) ).
tcf(c_102678,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK21(sK1,X0)) ),
inference(superposition,[status(thm)],[c_6673,c_70]) ).
tcf(c_102679,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| element(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_6673,c_69]) ).
tcf(c_102680,plain,
! [X0: $i] :
( in(sK21(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_6673,c_67]) ).
tcf(c_102682,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_12766]) ).
tcf(c_102683,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_12765]) ).
tcf(c_102684,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_10203]) ).
tcf(c_102685,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_10202]) ).
tcf(c_102686,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_6249]) ).
tcf(c_102687,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_5349]) ).
tcf(c_102689,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_12284]) ).
tcf(c_102690,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_4619]) ).
tcf(c_102691,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_4406]) ).
tcf(c_102700,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_6673,c_68472]) ).
tcf(c_102703,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK2) ),
inference(equality_factoring,[status(thm)],[c_6673]) ).
tcf(c_102705,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102703,c_61]) ).
tcf(c_102708,plain,
( in(sK21(sK1,sK12),relation_dom(sK2))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102700,c_95]) ).
tcf(c_102732,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_dom(sK2))
| in(sK21(sK1,relation_inverse(sK12)),relation_rng(sK12))
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102665,c_3610]) ).
tcf(c_102748,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102691,c_64]) ).
tcf(c_102752,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102690,c_64]) ).
tcf(c_102756,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102689,c_64]) ).
tcf(c_102777,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102687,c_64]) ).
tcf(c_102781,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102686,c_64]) ).
tcf(c_102785,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102685,c_64]) ).
tcf(c_102789,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102684,c_64]) ).
tcf(c_102793,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102683,c_64]) ).
tcf(c_102797,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102682,c_64]) ).
tcf(c_102947,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(relation_dom(sK2),sK21(sK1,sK2)) ),
inference(superposition,[status(thm)],[c_102705,c_70]) ).
tcf(c_102948,plain,
( element(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 ) ),
inference(superposition,[status(thm)],[c_102705,c_69]) ).
tcf(c_102951,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2))) = apply(sK1,sK15(sK1,sK21(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_102705,c_12335]) ).
tcf(c_102952,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK2)))) = sK15(sK1,sK21(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_102705,c_8396]) ).
tcf(c_102953,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK2)))) = sK15(sK1,sK21(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_102705,c_8395]) ).
tcf(c_102954,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102705,c_4044]) ).
tcf(c_102956,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102705,c_12701]) ).
tcf(c_102957,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102705,c_10144]) ).
tcf(c_102958,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK15(sK1,sK21(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_102705,c_4468]) ).
tcf(c_103050,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_28868,c_107]) ).
tcf(c_103051,plain,
( in(ordered_pair(apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_28868,c_4848]) ).
tcf(c_103053,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_28868,c_12678]) ).
tcf(c_103055,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_28868,c_59117]) ).
tcf(c_103056,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_28868,c_58270]) ).
tcf(c_103058,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_28868,c_34537]) ).
tcf(c_103059,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_28868,c_14876]) ).
tcf(c_103060,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(relation_dom(sK1),sK21(sK1,sK1))
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_28868,c_8391]) ).
tcf(c_103101,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_103050,c_4013]) ).
tcf(c_103147,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35648]) ).
tcf(c_103148,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35648]) ).
tcf(c_103149,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35648]) ).
tcf(c_103150,plain,
relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35648]) ).
tcf(c_103151,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35648]) ).
tcf(c_103152,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35648]) ).
tcf(c_103153,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35648]) ).
tcf(c_103154,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35648]) ).
tcf(c_103155,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35648]) ).
tcf(c_103156,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35648]) ).
tcf(c_103157,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35648]) ).
tcf(c_103158,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35648]) ).
tcf(c_103159,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35648]) ).
tcf(c_103160,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35648]) ).
tcf(c_103161,plain,
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35648]) ).
tcf(c_103162,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35648]) ).
tcf(c_103163,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35648]) ).
tcf(c_103164,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35648]) ).
tcf(c_103412,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35907]) ).
tcf(c_103413,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35907]) ).
tcf(c_103414,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35907]) ).
tcf(c_103415,plain,
relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35907]) ).
tcf(c_103416,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35907]) ).
tcf(c_103417,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35907]) ).
tcf(c_103418,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35907]) ).
tcf(c_103419,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35907]) ).
tcf(c_103420,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35907]) ).
tcf(c_103421,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35907]) ).
tcf(c_103422,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35907]) ).
tcf(c_103423,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35907]) ).
tcf(c_103424,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35907]) ).
tcf(c_103425,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35907]) ).
tcf(c_103426,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35907]) ).
tcf(c_103427,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35907]) ).
tcf(c_103428,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35907]) ).
tcf(c_103429,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35907]) ).
tcf(c_103469,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35908]) ).
tcf(c_103470,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35908]) ).
tcf(c_103471,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35908]) ).
tcf(c_103472,plain,
relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35908]) ).
tcf(c_103473,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35908]) ).
tcf(c_103474,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35908]) ).
tcf(c_103475,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35908]) ).
tcf(c_103476,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35908]) ).
tcf(c_103477,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35908]) ).
tcf(c_103478,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35908]) ).
tcf(c_103479,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35908]) ).
tcf(c_103480,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35908]) ).
tcf(c_103481,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35908]) ).
tcf(c_103482,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35908]) ).
tcf(c_103483,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35908]) ).
tcf(c_103484,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35908]) ).
tcf(c_103485,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35908]) ).
tcf(c_103486,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35908]) ).
tcf(c_103531,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK1),sK7(relation_inverse(sK1),X0)) ),
inference(superposition,[status(thm)],[c_10129,c_70]) ).
tcf(c_103532,plain,
! [X0: $i] :
( element(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_69]) ).
tcf(c_103535,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0)))) = apply(sK1,sK7(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_12766]) ).
tcf(c_103536,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0)))) = sK7(sK1,sK7(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_12765]) ).
tcf(c_103537,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0)))) = apply(sK1,sK7(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_10203]) ).
tcf(c_103538,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0)))) = sK7(sK1,sK7(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_10202]) ).
tcf(c_103539,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))) = sK15(sK1,apply(sK1,sK7(relation_inverse(sK1),X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_6249]) ).
tcf(c_103540,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0))) = sK15(sK1,sK7(sK1,sK7(relation_inverse(sK1),X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_5349]) ).
tcf(c_103542,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK7(relation_inverse(sK1),X0)) = apply(sK1,sK7(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_12284]) ).
tcf(c_103543,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_4619]) ).
tcf(c_103544,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_4406]) ).
tcf(c_103545,plain,
! [X0: $i] :
( ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_10129,c_10491]) ).
tcf(c_103547,plain,
! [X0: $i] :
( element(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_10492]) ).
tcf(c_103663,plain,
( in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12316,c_12272]) ).
tcf(c_103664,plain,
( in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12330,c_12272]) ).
tcf(c_103665,plain,
( in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12332,c_12272]) ).
tcf(c_103666,plain,
! [X0: $i] :
( in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_62859,c_12272]) ).
tcf(c_103667,plain,
( in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK14(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12336,c_12272]) ).
tcf(c_103675,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK1))
| ~ in(relation_dom(sK2),sK15(relation_inverse(sK1),X0)) ),
inference(superposition,[status(thm)],[c_12272,c_70]) ).
tcf(c_103676,plain,
! [X0: $i] :
( element(sK15(relation_inverse(sK1),X0),relation_dom(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_69]) ).
tcf(c_103679,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),sK15(sK1,sK15(relation_inverse(sK1),X0))) = apply(sK1,sK15(sK1,sK15(relation_inverse(sK1),X0))) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_12335]) ).
tcf(c_103680,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK15(relation_inverse(sK1),X0)))) = sK15(sK1,sK15(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_8396]) ).
tcf(c_103681,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK15(relation_inverse(sK1),X0)))) = sK15(sK1,sK15(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_8395]) ).
tcf(c_103682,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK15(relation_inverse(sK1),X0))) = sK15(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_4044]) ).
tcf(c_103683,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK2),sK15(relation_inverse(sK1),X0)) = apply(sK2,sK15(relation_inverse(sK1),X0)) )
| ~ relation(relation_inverse(sK2))
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_42224]) ).
tcf(c_103684,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK15(relation_inverse(sK1),X0))) = sK15(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_12701]) ).
tcf(c_103685,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK15(relation_inverse(sK1),X0))) = sK15(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_10144]) ).
tcf(c_103686,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK15(relation_inverse(sK1),X0)) = sK15(sK1,sK15(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_12272,c_4468]) ).
tcf(c_103781,plain,
! [X0: $i] :
( in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_55855,c_12688]) ).
tcf(c_103785,plain,
! [X0: $i] :
( in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_56725,c_12688]) ).
tcf(c_103791,plain,
( in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13935,c_12688]) ).
tcf(c_103792,plain,
( in(sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13933,c_12688]) ).
tcf(c_103793,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12634,c_12688]) ).
tcf(c_103795,plain,
( in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18307,c_12688]) ).
tcf(c_103796,plain,
( in(sK15(sK1,sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_18305,c_12688]) ).
tcf(c_103797,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_17971,c_12688]) ).
tcf(c_103799,plain,
( in(sK15(sK1,sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_7060,c_12688]) ).
tcf(c_103801,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6420,c_12688]) ).
tcf(c_103802,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_6421,c_12688]) ).
tcf(c_103804,plain,
( in(sK15(sK1,sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_9987,c_12688]) ).
tcf(c_103810,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_58270,c_12688]) ).
tcf(c_103811,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_59117,c_12688]) ).
tcf(c_103820,plain,
( in(sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13387,c_12688]) ).
tcf(c_103823,plain,
( in(sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14034,c_12688]) ).
tcf(c_103825,plain,
! [X0: $i] :
( ~ in(X0,relation_dom(sK2))
| ~ in(relation_dom(sK1),apply(relation_inverse(sK1),X0)) ),
inference(superposition,[status(thm)],[c_12688,c_70]) ).
tcf(c_103826,plain,
! [X0: $i] :
( element(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_69]) ).
tcf(c_103829,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0)))) = apply(sK1,apply(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_12766]) ).
tcf(c_103830,plain,
! [X0: $i] :
( ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0)))) = sK7(sK1,apply(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_12765]) ).
tcf(c_103831,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0)))) = apply(sK1,apply(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_10203]) ).
tcf(c_103832,plain,
! [X0: $i] :
( ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0)))) = sK7(sK1,apply(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_10202]) ).
tcf(c_103833,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))) = sK15(sK1,apply(sK1,apply(relation_inverse(sK1),X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_6249]) ).
tcf(c_103834,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0))) = sK15(sK1,sK7(sK1,apply(relation_inverse(sK1),X0))) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_5349]) ).
tcf(c_103836,plain,
! [X0: $i] :
( ( sK15(relation_inverse(sK1),apply(relation_inverse(sK1),X0)) = apply(sK1,apply(relation_inverse(sK1),X0)) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_12284]) ).
tcf(c_103837,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_4619]) ).
tcf(c_103838,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK7(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_4406]) ).
tcf(c_104276,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102748,c_70]) ).
tcf(c_104277,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_69]) ).
tcf(c_104280,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_12335]) ).
tcf(c_104281,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102748,c_8396]) ).
tcf(c_104282,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102748,c_8395]) ).
tcf(c_104283,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_4044]) ).
tcf(c_104284,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102748,c_42224]) ).
tcf(c_104285,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_12701]) ).
tcf(c_104286,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_10144]) ).
tcf(c_104287,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102748,c_4468]) ).
tcf(c_104326,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102752,c_70]) ).
tcf(c_104327,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_69]) ).
tcf(c_104330,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_12335]) ).
tcf(c_104331,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102752,c_8396]) ).
tcf(c_104332,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102752,c_8395]) ).
tcf(c_104333,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_4044]) ).
tcf(c_104334,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102752,c_42224]) ).
tcf(c_104335,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_12701]) ).
tcf(c_104336,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_10144]) ).
tcf(c_104337,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102752,c_4468]) ).
tcf(c_104376,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102756,c_70]) ).
tcf(c_104377,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102756,c_69]) ).
tcf(c_104380,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102756,c_12335]) ).
tcf(c_104381,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102756,c_8396]) ).
tcf(c_104382,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102756,c_8395]) ).
tcf(c_104383,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102756,c_4044]) ).
tcf(c_104384,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102756,c_42224]) ).
tcf(c_104385,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102756,c_12701]) ).
tcf(c_104386,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102756,c_10144]) ).
tcf(c_104387,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102756,c_4468]) ).
tcf(c_104487,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102777,c_70]) ).
tcf(c_104488,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_69]) ).
tcf(c_104491,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_12335]) ).
tcf(c_104492,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102777,c_8396]) ).
tcf(c_104493,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102777,c_8395]) ).
tcf(c_104494,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_4044]) ).
tcf(c_104495,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102777,c_42224]) ).
tcf(c_104496,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_12701]) ).
tcf(c_104497,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_10144]) ).
tcf(c_104498,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102777,c_4468]) ).
tcf(c_104537,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102781,c_70]) ).
tcf(c_104538,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_69]) ).
tcf(c_104541,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_12335]) ).
tcf(c_104542,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102781,c_8396]) ).
tcf(c_104543,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102781,c_8395]) ).
tcf(c_104544,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_4044]) ).
tcf(c_104545,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102781,c_42224]) ).
tcf(c_104546,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_12701]) ).
tcf(c_104547,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_10144]) ).
tcf(c_104548,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102781,c_4468]) ).
tcf(c_104587,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102785,c_70]) ).
tcf(c_104588,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_69]) ).
tcf(c_104591,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_12335]) ).
tcf(c_104592,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_8396]) ).
tcf(c_104593,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_8395]) ).
tcf(c_104594,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_4044]) ).
tcf(c_104595,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102785,c_42224]) ).
tcf(c_104596,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_12701]) ).
tcf(c_104597,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_10144]) ).
tcf(c_104598,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102785,c_4468]) ).
tcf(c_104637,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102789,c_70]) ).
tcf(c_104638,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_69]) ).
tcf(c_104641,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_12335]) ).
tcf(c_104642,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_8396]) ).
tcf(c_104643,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_8395]) ).
tcf(c_104644,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_4044]) ).
tcf(c_104645,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102789,c_42224]) ).
tcf(c_104646,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_12701]) ).
tcf(c_104647,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_10144]) ).
tcf(c_104648,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102789,c_4468]) ).
tcf(c_104694,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK7(sK1,sK21(sK1,sK1)) = apply(sK1,empty_set) )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_29377,c_52427]) ).
tcf(c_104695,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29377,c_19430]) ).
tcf(c_104696,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29377,c_4045]) ).
tcf(c_104697,plain,
( element(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29377,c_19431]) ).
tcf(c_104698,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29377,c_18734]) ).
tcf(c_104699,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29377,c_87]) ).
tcf(c_104723,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_104699,c_62,c_61]) ).
tcf(c_104754,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35909]) ).
tcf(c_104755,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35909]) ).
tcf(c_104756,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35909]) ).
tcf(c_104757,plain,
relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35909]) ).
tcf(c_104758,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35909]) ).
tcf(c_104759,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35909]) ).
tcf(c_104760,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35909]) ).
tcf(c_104761,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35909]) ).
tcf(c_104762,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35909]) ).
tcf(c_104763,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35909]) ).
tcf(c_104764,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35909]) ).
tcf(c_104765,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35909]) ).
tcf(c_104766,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35909]) ).
tcf(c_104767,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35909]) ).
tcf(c_104768,plain,
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35909]) ).
tcf(c_104769,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35909]) ).
tcf(c_104770,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35909]) ).
tcf(c_104771,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35909]) ).
tcf(c_105018,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35979]) ).
tcf(c_105019,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35979]) ).
tcf(c_105020,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35979]) ).
tcf(c_105021,plain,
relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35979]) ).
tcf(c_105022,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35979]) ).
tcf(c_105023,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35979]) ).
tcf(c_105024,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35979]) ).
tcf(c_105025,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35979]) ).
tcf(c_105026,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35979]) ).
tcf(c_105027,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35979]) ).
tcf(c_105028,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35979]) ).
tcf(c_105029,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35979]) ).
tcf(c_105030,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35979]) ).
tcf(c_105031,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35979]) ).
tcf(c_105032,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35979]) ).
tcf(c_105033,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35979]) ).
tcf(c_105034,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35979]) ).
tcf(c_105035,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35979]) ).
tcf(c_105140,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35980]) ).
tcf(c_105141,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35980]) ).
tcf(c_105142,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35980]) ).
tcf(c_105143,plain,
relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35980]) ).
tcf(c_105144,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35980]) ).
tcf(c_105145,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35980]) ).
tcf(c_105146,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35980]) ).
tcf(c_105147,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35980]) ).
tcf(c_105148,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35980]) ).
tcf(c_105149,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35980]) ).
tcf(c_105150,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35980]) ).
tcf(c_105151,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35980]) ).
tcf(c_105152,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35980]) ).
tcf(c_105153,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35980]) ).
tcf(c_105154,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35980]) ).
tcf(c_105155,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35980]) ).
tcf(c_105156,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35980]) ).
tcf(c_105157,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35980]) ).
tcf(c_105226,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35981]) ).
tcf(c_105227,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35981]) ).
tcf(c_105228,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35981]) ).
tcf(c_105229,plain,
relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35981]) ).
tcf(c_105230,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35981]) ).
tcf(c_105231,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35981]) ).
tcf(c_105232,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35981]) ).
tcf(c_105233,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35981]) ).
tcf(c_105234,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35981]) ).
tcf(c_105235,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35981]) ).
tcf(c_105236,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35981]) ).
tcf(c_105237,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35981]) ).
tcf(c_105238,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35981]) ).
tcf(c_105239,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35981]) ).
tcf(c_105240,plain,
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35981]) ).
tcf(c_105241,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35981]) ).
tcf(c_105242,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35981]) ).
tcf(c_105243,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35981]) ).
tcf(c_105365,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15887]) ).
tcf(c_105366,plain,
relation_dom(relation_dom(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15887]) ).
tcf(c_105369,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15887]) ).
tcf(c_105370,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15887]) ).
tcf(c_105371,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15887]) ).
tcf(c_105372,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15887]) ).
tcf(c_105373,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15887]) ).
tcf(c_105374,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15887]) ).
tcf(c_105375,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15887]) ).
tcf(c_105376,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15887]) ).
tcf(c_105377,plain,
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15887]) ).
tcf(c_105378,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15887]) ).
tcf(c_105380,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15887]) ).
tcf(c_105412,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15924]) ).
tcf(c_105413,plain,
relation_dom(relation_dom(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15924]) ).
tcf(c_105416,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15924]) ).
tcf(c_105417,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15924]) ).
tcf(c_105418,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15924]) ).
tcf(c_105419,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15924]) ).
tcf(c_105420,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15924]) ).
tcf(c_105421,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15924]) ).
tcf(c_105422,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15924]) ).
tcf(c_105423,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15924]) ).
tcf(c_105424,plain,
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15924]) ).
tcf(c_105425,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15924]) ).
tcf(c_105427,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15924]) ).
tcf(c_105459,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102793,c_70]) ).
tcf(c_105460,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_69]) ).
tcf(c_105463,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_12335]) ).
tcf(c_105464,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_8396]) ).
tcf(c_105465,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_8395]) ).
tcf(c_105466,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_4044]) ).
tcf(c_105467,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102793,c_42224]) ).
tcf(c_105468,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_12701]) ).
tcf(c_105469,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_10144]) ).
tcf(c_105470,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102793,c_4468]) ).
tcf(c_105509,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102797,c_70]) ).
tcf(c_105510,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_69]) ).
tcf(c_105513,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_12335]) ).
tcf(c_105514,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_8396]) ).
tcf(c_105515,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_8395]) ).
tcf(c_105516,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_4044]) ).
tcf(c_105517,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102797,c_42224]) ).
tcf(c_105518,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_12701]) ).
tcf(c_105519,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_10144]) ).
tcf(c_105520,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102797,c_4468]) ).
tcf(c_105564,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ in(sK2,ordered_pair(sK7(sK1,sK21(sK1,sK1)),empty_set)) ),
inference(superposition,[status(thm)],[c_104723,c_70]) ).
tcf(c_105565,plain,
( element(ordered_pair(sK7(sK1,sK21(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_104723,c_69]) ).
tcf(c_105567,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ relation(sK2)
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_104723,c_106]) ).
tcf(c_105572,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105567,c_61]) ).
tcf(c_105601,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_105572]) ).
tcf(c_105619,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102954,c_87]) ).
tcf(c_105620,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(sK2,sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102954,c_100631]) ).
tcf(c_105621,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102954,c_64920]) ).
tcf(c_105622,plain,
( in(ordered_pair(sK21(sK1,sK2),apply(sK2,sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102954,c_12604]) ).
tcf(c_105623,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102954,c_12599]) ).
tcf(c_105624,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(sK2,sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102954,c_61586]) ).
tcf(c_105625,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102954,c_61136]) ).
tcf(c_105626,plain,
( in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102954,c_57811]) ).
tcf(c_105627,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,sK2)) = sK15(sK1,sK21(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102954,c_57193]) ).
tcf(c_105634,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102954,c_4791]) ).
tcf(c_105658,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105619,c_65,c_64]) ).
tcf(c_105700,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2))) ),
inference(superposition,[status(thm)],[c_105658,c_70]) ).
tcf(c_105701,plain,
( element(ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105658,c_69]) ).
tcf(c_105703,plain,
( in(sK21(sK1,sK2),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105658,c_106]) ).
tcf(c_105708,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105658,c_3784]) ).
tcf(c_105709,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_105703,c_4013]) ).
tcf(c_105724,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_9713,c_102956]) ).
tcf(c_105725,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,sK2)) = empty_set )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_4763,c_102956]) ).
tcf(c_105729,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102956,c_87]) ).
tcf(c_105730,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102956,c_100631]) ).
tcf(c_105731,plain,
( in(ordered_pair(sK21(sK1,sK2),apply(relation_inverse(sK1),sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102956,c_12604]) ).
tcf(c_105732,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102956,c_12599]) ).
tcf(c_105733,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102956,c_61586]) ).
tcf(c_105735,plain,
( in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102956,c_57811]) ).
tcf(c_105764,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_105729,c_65,c_64]) ).
tcf(c_105967,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_29379,c_107]) ).
tcf(c_105968,plain,
( in(ordered_pair(sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29379,c_4848]) ).
tcf(c_105970,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29379,c_12678]) ).
tcf(c_105972,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_29379,c_59117]) ).
tcf(c_105973,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_29379,c_58270]) ).
tcf(c_105975,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_29379,c_34537]) ).
tcf(c_105976,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_29379,c_14876]) ).
tcf(c_105978,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(relation_dom(sK1),sK21(sK1,sK1))
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29379,c_8391]) ).
tcf(c_105981,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_29379,c_71817]) ).
tcf(c_106021,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_105967,c_4013]) ).
tcf(c_106034,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35997]) ).
tcf(c_106035,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35997]) ).
tcf(c_106036,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35997]) ).
tcf(c_106037,plain,
relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35997]) ).
tcf(c_106038,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35997]) ).
tcf(c_106039,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35997]) ).
tcf(c_106040,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35997]) ).
tcf(c_106041,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35997]) ).
tcf(c_106042,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35997]) ).
tcf(c_106043,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35997]) ).
tcf(c_106044,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35997]) ).
tcf(c_106045,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35997]) ).
tcf(c_106046,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35997]) ).
tcf(c_106047,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35997]) ).
tcf(c_106048,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35997]) ).
tcf(c_106049,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35997]) ).
tcf(c_106050,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35997]) ).
tcf(c_106051,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35997]) ).
tcf(c_106133,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35998]) ).
tcf(c_106134,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35998]) ).
tcf(c_106135,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35998]) ).
tcf(c_106136,plain,
relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35998]) ).
tcf(c_106137,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35998]) ).
tcf(c_106138,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35998]) ).
tcf(c_106139,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35998]) ).
tcf(c_106140,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35998]) ).
tcf(c_106141,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35998]) ).
tcf(c_106142,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35998]) ).
tcf(c_106143,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35998]) ).
tcf(c_106144,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35998]) ).
tcf(c_106145,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35998]) ).
tcf(c_106146,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35998]) ).
tcf(c_106147,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35998]) ).
tcf(c_106148,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35998]) ).
tcf(c_106149,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35998]) ).
tcf(c_106150,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35998]) ).
tcf(c_106190,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_35999]) ).
tcf(c_106191,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_35999]) ).
tcf(c_106192,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_35999]) ).
tcf(c_106193,plain,
relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_35999]) ).
tcf(c_106194,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_35999]) ).
tcf(c_106195,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_35999]) ).
tcf(c_106196,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_35999]) ).
tcf(c_106197,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_35999]) ).
tcf(c_106198,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_35999]) ).
tcf(c_106199,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_35999]) ).
tcf(c_106200,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_35999]) ).
tcf(c_106201,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_35999]) ).
tcf(c_106202,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_35999]) ).
tcf(c_106203,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_35999]) ).
tcf(c_106204,plain,
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_35999]) ).
tcf(c_106205,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_35999]) ).
tcf(c_106206,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_35999]) ).
tcf(c_106207,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_35999]) ).
tcf(c_106305,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_36023]) ).
tcf(c_106306,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_36023]) ).
tcf(c_106307,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_36023]) ).
tcf(c_106308,plain,
relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_36023]) ).
tcf(c_106309,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_36023]) ).
tcf(c_106310,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_36023]) ).
tcf(c_106311,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_36023]) ).
tcf(c_106312,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_36023]) ).
tcf(c_106313,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_36023]) ).
tcf(c_106314,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_36023]) ).
tcf(c_106315,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_36023]) ).
tcf(c_106316,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_36023]) ).
tcf(c_106317,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_36023]) ).
tcf(c_106318,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_36023]) ).
tcf(c_106319,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_36023]) ).
tcf(c_106320,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_36023]) ).
tcf(c_106321,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_36023]) ).
tcf(c_106322,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_36023]) ).
tcf(c_106364,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_15959]) ).
tcf(c_106365,plain,
relation_dom(relation_dom(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_15959]) ).
tcf(c_106368,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_15959]) ).
tcf(c_106369,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_15959]) ).
tcf(c_106370,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_15959]) ).
tcf(c_106371,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_15959]) ).
tcf(c_106372,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_15959]) ).
tcf(c_106373,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_15959]) ).
tcf(c_106374,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_15959]) ).
tcf(c_106375,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_15959]) ).
tcf(c_106376,plain,
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_15959]) ).
tcf(c_106377,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_15959]) ).
tcf(c_106379,plain,
! [X0: $i] :
( ( relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_15959]) ).
tcf(c_106434,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_16062]) ).
tcf(c_106435,plain,
relation_dom(relation_rng(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_16062]) ).
tcf(c_106438,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_16062]) ).
tcf(c_106439,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_16062]) ).
tcf(c_106440,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_16062]) ).
tcf(c_106441,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_16062]) ).
tcf(c_106442,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_16062]) ).
tcf(c_106443,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_16062]) ).
tcf(c_106444,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_16062]) ).
tcf(c_106445,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_16062]) ).
tcf(c_106446,plain,
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_16062]) ).
tcf(c_106447,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_16062]) ).
tcf(c_106449,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_16062]) ).
tcf(c_106481,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17552]) ).
tcf(c_106482,plain,
relation_dom(relation_rng(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17552]) ).
tcf(c_106485,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17552]) ).
tcf(c_106486,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17552]) ).
tcf(c_106487,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17552]) ).
tcf(c_106488,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17552]) ).
tcf(c_106489,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17552]) ).
tcf(c_106490,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17552]) ).
tcf(c_106491,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17552]) ).
tcf(c_106492,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17552]) ).
tcf(c_106493,plain,
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17552]) ).
tcf(c_106494,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17552]) ).
tcf(c_106496,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17552]) ).
tcf(c_106551,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17587]) ).
tcf(c_106552,plain,
relation_dom(relation_rng(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17587]) ).
tcf(c_106555,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17587]) ).
tcf(c_106556,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17587]) ).
tcf(c_106557,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17587]) ).
tcf(c_106558,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17587]) ).
tcf(c_106559,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17587]) ).
tcf(c_106560,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17587]) ).
tcf(c_106561,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17587]) ).
tcf(c_106562,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17587]) ).
tcf(c_106563,plain,
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17587]) ).
tcf(c_106564,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17587]) ).
tcf(c_106566,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17587]) ).
tcf(c_106664,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_105764]) ).
tcf(c_106665,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,sK2)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_105764]) ).
tcf(c_106666,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2))) ),
inference(superposition,[status(thm)],[c_105764,c_70]) ).
tcf(c_106667,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105764,c_69]) ).
tcf(c_106669,plain,
( in(sK21(sK1,sK2),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105764,c_106]) ).
tcf(c_106675,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_106669,c_4013]) ).
tcf(c_106696,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_34013,c_102957]) ).
tcf(c_106700,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102957,c_87]) ).
tcf(c_106701,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102957,c_100631]) ).
tcf(c_106702,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102957,c_64920]) ).
tcf(c_106703,plain,
( in(ordered_pair(sK21(sK1,sK2),sK7(relation_inverse(sK1),sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102957,c_12604]) ).
tcf(c_106704,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102957,c_12599]) ).
tcf(c_106705,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102957,c_61586]) ).
tcf(c_106706,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102957,c_57811]) ).
tcf(c_106707,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK21(sK1,sK2)) = sK15(sK1,sK21(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102957,c_57193]) ).
tcf(c_106715,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK7(relation_inverse(sK1),sK21(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102957,c_4791]) ).
tcf(c_106716,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,sK2) = empty_set )
| ( apply(sK2,sK21(sK1,sK2)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK7(relation_inverse(sK1),sK21(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_102957,c_10494]) ).
tcf(c_106747,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106700,c_65,c_64]) ).
tcf(c_106850,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_106747]) ).
tcf(c_106851,plain,
( ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2))) ),
inference(superposition,[status(thm)],[c_106747,c_70]) ).
tcf(c_106852,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_106747,c_69]) ).
tcf(c_106854,plain,
( in(sK21(sK1,sK2),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_106747,c_106]) ).
tcf(c_106859,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = sK7(relation_inverse(sK1),sK21(sK1,sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_106747,c_3784]) ).
tcf(c_106860,plain,
( in(sK21(sK1,sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_106854,c_4013]) ).
tcf(c_106882,plain,
( in(ordered_pair(sK21(sK1,sK2),sK15(sK1,sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK2),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_102958,c_87]) ).
tcf(c_106883,plain,
( in(sK15(sK1,sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102958,c_12688]) ).
tcf(c_106884,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,sK2)) = empty_set )
| ~ in(relation_dom(sK2),sK21(sK1,sK2))
| ~ in(sK15(sK1,sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102958,c_13471]) ).
tcf(c_106887,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2))) ),
inference(superposition,[status(thm)],[c_102958,c_34564]) ).
tcf(c_106888,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_102958,c_34565]) ).
tcf(c_106889,plain,
( in(sK15(sK1,sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_102958,c_34571]) ).
tcf(c_106890,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_102958,c_34529]) ).
tcf(c_106894,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102958,c_4623]) ).
tcf(c_106895,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_102958,c_105764]) ).
tcf(c_106896,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK21(sK1,sK2))) = sK21(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_102958,c_102956]) ).
tcf(c_106927,plain,
( in(ordered_pair(sK21(sK1,sK2),sK15(sK1,sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_106882,c_4030]) ).
tcf(c_106928,plain,
( in(ordered_pair(sK21(sK1,sK2),sK15(sK1,sK21(sK1,sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106927,c_987,c_3611]) ).
tcf(c_106956,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_7118]) ).
tcf(c_106957,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_7118]) ).
tcf(c_106958,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK22(relation_inverse(sK9),sK1),relation_dom(sK2))
| ( relation_inverse(relation_inverse(sK9)) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_7118]) ).
tcf(c_106959,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK22(relation_inverse(sK10),sK1),relation_dom(sK2))
| ( relation_inverse(relation_inverse(sK10)) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_7118]) ).
tcf(c_106961,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK21(X0,sK1)) ),
inference(superposition,[status(thm)],[c_7118,c_70]) ).
tcf(c_106962,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| element(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7118,c_69]) ).
tcf(c_106963,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_7118,c_67]) ).
tcf(c_106964,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK1))) = sK21(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_7118,c_43161]) ).
tcf(c_106965,plain,
( in(sK22(sK9,sK1),relation_dom(sK2))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_7118,c_29938]) ).
tcf(c_106966,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_7118,c_69454]) ).
tcf(c_106968,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106966,c_95]) ).
tcf(c_106972,plain,
( in(sK22(sK9,sK1),relation_dom(sK2))
| ( relation_inverse(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106965,c_83]) ).
tcf(c_106988,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK22(relation_inverse(sK10),sK1),relation_dom(sK2))
| ( sK1 = sK10 )
| ~ relation(relation_inverse(sK10)) ),
inference(light_normalisation,[status(thm)],[c_106959,c_3628]) ).
tcf(c_106993,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK22(relation_inverse(sK9),sK1),relation_dom(sK2))
| ( sK1 = sK9 )
| ~ relation(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_106958,c_3627]) ).
tcf(c_106998,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_106957,c_3624]) ).
tcf(c_107003,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_106956,c_3629]) ).
tcf(c_107004,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107003,c_3610]) ).
tcf(c_107008,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK1))) = sK21(sK2,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_106964,c_61]) ).
tcf(c_107254,plain,
( in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_7119]) ).
tcf(c_107255,plain,
( in(sK22(relation_inverse(sK9),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( relation_inverse(relation_inverse(sK9)) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_7119]) ).
tcf(c_107256,plain,
( in(sK22(relation_inverse(sK10),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( relation_inverse(relation_inverse(sK10)) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_7119]) ).
tcf(c_107257,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_7119]) ).
tcf(c_107258,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK2),sK22(X0,sK1)) ),
inference(superposition,[status(thm)],[c_7119,c_70]) ).
tcf(c_107259,plain,
! [X0: $i] :
( element(sK22(X0,sK1),relation_dom(sK2))
| in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_69]) ).
tcf(c_107262,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(X0,sK1))) = apply(sK1,sK15(sK1,sK22(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_12335]) ).
tcf(c_107263,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(X0,sK1)))) = sK15(sK1,sK22(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_8396]) ).
tcf(c_107264,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(X0,sK1)))) = sK15(sK1,sK22(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_8395]) ).
tcf(c_107265,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(sK2,sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_4044]) ).
tcf(c_107266,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(X0,sK1)) = apply(sK2,sK22(X0,sK1)) )
| ~ relation(X0)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_7119,c_42224]) ).
tcf(c_107267,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_12701]) ).
tcf(c_107268,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(X0,sK1))) = sK22(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_10144]) ).
tcf(c_107269,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK22(X0,sK1)) = sK15(sK1,sK22(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_4468]) ).
tcf(c_107270,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK22(X0,sK1)) ),
inference(superposition,[status(thm)],[c_7119,c_70]) ).
tcf(c_107271,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| element(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_7119,c_69]) ).
tcf(c_107272,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(sK2))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_7119,c_67]) ).
tcf(c_107274,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_12766]) ).
tcf(c_107275,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_12765]) ).
tcf(c_107276,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_10203]) ).
tcf(c_107277,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_10202]) ).
tcf(c_107278,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_6249]) ).
tcf(c_107279,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_5349]) ).
tcf(c_107281,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_12284]) ).
tcf(c_107282,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_4619]) ).
tcf(c_107283,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_4406]) ).
tcf(c_107292,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_7119,c_68472]) ).
tcf(c_107295,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK2) ),
inference(equality_factoring,[status(thm)],[c_7119]) ).
tcf(c_107297,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107295,c_61]) ).
tcf(c_107300,plain,
( in(sK22(sK12,sK1),relation_dom(sK2))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107292,c_95]) ).
tcf(c_107324,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_107257,c_3629]) ).
tcf(c_107325,plain,
( in(sK22(relation_inverse(sK12),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107324,c_3610]) ).
tcf(c_107329,plain,
( in(sK22(relation_inverse(sK10),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( sK1 = sK10 )
| ~ relation(relation_inverse(sK10)) ),
inference(light_normalisation,[status(thm)],[c_107256,c_3628]) ).
tcf(c_107334,plain,
( in(sK22(relation_inverse(sK9),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( sK1 = sK9 )
| ~ relation(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_107255,c_3627]) ).
tcf(c_107339,plain,
( in(sK22(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK22(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_107254,c_3624]) ).
tcf(c_107344,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107283,c_64]) ).
tcf(c_107348,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107282,c_64]) ).
tcf(c_107352,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107281,c_64]) ).
tcf(c_107373,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107279,c_64]) ).
tcf(c_107377,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107278,c_64]) ).
tcf(c_107381,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107277,c_64]) ).
tcf(c_107385,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107276,c_64]) ).
tcf(c_107389,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107275,c_64]) ).
tcf(c_107393,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107274,c_64]) ).
tcf(c_107465,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_29763,c_107]) ).
tcf(c_107466,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29763,c_4848]) ).
tcf(c_107468,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29763,c_12678]) ).
tcf(c_107470,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_29763,c_59117]) ).
tcf(c_107471,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_29763,c_58270]) ).
tcf(c_107473,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_29763,c_34537]) ).
tcf(c_107474,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_29763,c_14876]) ).
tcf(c_107475,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(relation_dom(sK1),sK22(sK1,sK1))
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_29763,c_8391]) ).
tcf(c_107516,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_107465,c_4013]) ).
tcf(c_107769,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_36024]) ).
tcf(c_107770,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_36024]) ).
tcf(c_107771,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_36024]) ).
tcf(c_107772,plain,
relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_36024]) ).
tcf(c_107773,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_36024]) ).
tcf(c_107774,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_36024]) ).
tcf(c_107775,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_36024]) ).
tcf(c_107776,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_36024]) ).
tcf(c_107777,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_36024]) ).
tcf(c_107778,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_36024]) ).
tcf(c_107779,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_36024]) ).
tcf(c_107780,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_36024]) ).
tcf(c_107781,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_36024]) ).
tcf(c_107782,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_36024]) ).
tcf(c_107783,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_36024]) ).
tcf(c_107784,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_36024]) ).
tcf(c_107785,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_36024]) ).
tcf(c_107786,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_36024]) ).
tcf(c_107852,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_36025]) ).
tcf(c_107853,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_36025]) ).
tcf(c_107854,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_36025]) ).
tcf(c_107855,plain,
relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_36025]) ).
tcf(c_107856,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_36025]) ).
tcf(c_107857,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_36025]) ).
tcf(c_107858,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_36025]) ).
tcf(c_107859,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_36025]) ).
tcf(c_107860,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_36025]) ).
tcf(c_107861,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_36025]) ).
tcf(c_107862,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_36025]) ).
tcf(c_107863,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_36025]) ).
tcf(c_107864,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_36025]) ).
tcf(c_107865,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_36025]) ).
tcf(c_107866,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_36025]) ).
tcf(c_107867,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_36025]) ).
tcf(c_107868,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_36025]) ).
tcf(c_107869,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_36025]) ).
tcf(c_108078,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37927]) ).
tcf(c_108079,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37927]) ).
tcf(c_108080,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37927]) ).
tcf(c_108081,plain,
relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37927]) ).
tcf(c_108082,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37927]) ).
tcf(c_108083,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37927]) ).
tcf(c_108084,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37927]) ).
tcf(c_108085,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37927]) ).
tcf(c_108086,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37927]) ).
tcf(c_108087,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37927]) ).
tcf(c_108088,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37927]) ).
tcf(c_108089,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37927]) ).
tcf(c_108090,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37927]) ).
tcf(c_108091,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37927]) ).
tcf(c_108092,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37927]) ).
tcf(c_108093,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37927]) ).
tcf(c_108094,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37927]) ).
tcf(c_108095,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37927]) ).
tcf(c_108135,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37928]) ).
tcf(c_108136,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37928]) ).
tcf(c_108137,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37928]) ).
tcf(c_108138,plain,
relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37928]) ).
tcf(c_108139,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37928]) ).
tcf(c_108140,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37928]) ).
tcf(c_108141,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37928]) ).
tcf(c_108142,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37928]) ).
tcf(c_108143,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37928]) ).
tcf(c_108144,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37928]) ).
tcf(c_108145,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37928]) ).
tcf(c_108146,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37928]) ).
tcf(c_108147,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37928]) ).
tcf(c_108148,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37928]) ).
tcf(c_108149,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37928]) ).
tcf(c_108150,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37928]) ).
tcf(c_108151,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37928]) ).
tcf(c_108152,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37928]) ).
tcf(c_108192,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ in(relation_dom(sK2),sK22(sK2,sK1)) ),
inference(superposition,[status(thm)],[c_107297,c_70]) ).
tcf(c_108193,plain,
( element(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 ) ),
inference(superposition,[status(thm)],[c_107297,c_69]) ).
tcf(c_108196,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1))) = apply(sK1,sK15(sK1,sK22(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_107297,c_12335]) ).
tcf(c_108197,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK2,sK1)))) = sK15(sK1,sK22(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_107297,c_8396]) ).
tcf(c_108198,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK2,sK1)))) = sK15(sK1,sK22(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_107297,c_8395]) ).
tcf(c_108199,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_107297,c_4044]) ).
tcf(c_108201,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_107297,c_12701]) ).
tcf(c_108202,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_107297,c_10144]) ).
tcf(c_108203,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK15(sK1,sK22(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_107297,c_4468]) ).
tcf(c_108234,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17631]) ).
tcf(c_108235,plain,
relation_dom(relation_inverse(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17631]) ).
tcf(c_108238,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17631]) ).
tcf(c_108239,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17631]) ).
tcf(c_108240,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17631]) ).
tcf(c_108241,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17631]) ).
tcf(c_108242,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17631]) ).
tcf(c_108243,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17631]) ).
tcf(c_108244,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17631]) ).
tcf(c_108245,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17631]) ).
tcf(c_108246,plain,
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17631]) ).
tcf(c_108247,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17631]) ).
tcf(c_108249,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17631]) ).
tcf(c_108281,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_17701]) ).
tcf(c_108282,plain,
relation_dom(relation_inverse(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_17701]) ).
tcf(c_108285,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_17701]) ).
tcf(c_108286,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_17701]) ).
tcf(c_108287,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_17701]) ).
tcf(c_108288,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_17701]) ).
tcf(c_108289,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_17701]) ).
tcf(c_108290,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_17701]) ).
tcf(c_108291,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_17701]) ).
tcf(c_108292,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_17701]) ).
tcf(c_108293,plain,
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_17701]) ).
tcf(c_108294,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_17701]) ).
tcf(c_108296,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_17701]) ).
tcf(c_108488,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107344,c_70]) ).
tcf(c_108489,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_69]) ).
tcf(c_108492,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_12335]) ).
tcf(c_108493,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107344,c_8396]) ).
tcf(c_108494,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107344,c_8395]) ).
tcf(c_108495,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_4044]) ).
tcf(c_108496,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107344,c_42224]) ).
tcf(c_108497,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_12701]) ).
tcf(c_108498,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_10144]) ).
tcf(c_108499,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107344,c_4468]) ).
tcf(c_108538,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107348,c_70]) ).
tcf(c_108539,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_69]) ).
tcf(c_108542,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_12335]) ).
tcf(c_108543,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107348,c_8396]) ).
tcf(c_108544,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107348,c_8395]) ).
tcf(c_108545,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_4044]) ).
tcf(c_108546,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107348,c_42224]) ).
tcf(c_108547,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_12701]) ).
tcf(c_108548,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_10144]) ).
tcf(c_108549,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107348,c_4468]) ).
tcf(c_108588,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107352,c_70]) ).
tcf(c_108589,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107352,c_69]) ).
tcf(c_108592,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107352,c_12335]) ).
tcf(c_108593,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107352,c_8396]) ).
tcf(c_108594,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107352,c_8395]) ).
tcf(c_108595,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107352,c_4044]) ).
tcf(c_108596,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107352,c_42224]) ).
tcf(c_108597,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107352,c_12701]) ).
tcf(c_108598,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107352,c_10144]) ).
tcf(c_108599,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107352,c_4468]) ).
tcf(c_108699,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107373,c_70]) ).
tcf(c_108700,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_69]) ).
tcf(c_108703,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_12335]) ).
tcf(c_108704,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107373,c_8396]) ).
tcf(c_108705,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107373,c_8395]) ).
tcf(c_108706,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_4044]) ).
tcf(c_108707,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107373,c_42224]) ).
tcf(c_108708,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_12701]) ).
tcf(c_108709,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_10144]) ).
tcf(c_108710,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107373,c_4468]) ).
tcf(c_108749,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107377,c_70]) ).
tcf(c_108750,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_69]) ).
tcf(c_108753,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_12335]) ).
tcf(c_108754,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107377,c_8396]) ).
tcf(c_108755,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107377,c_8395]) ).
tcf(c_108756,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_4044]) ).
tcf(c_108757,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107377,c_42224]) ).
tcf(c_108758,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_12701]) ).
tcf(c_108759,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_10144]) ).
tcf(c_108760,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107377,c_4468]) ).
tcf(c_108811,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107381,c_70]) ).
tcf(c_108812,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_69]) ).
tcf(c_108815,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_12335]) ).
tcf(c_108816,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_8396]) ).
tcf(c_108817,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_8395]) ).
tcf(c_108818,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_4044]) ).
tcf(c_108819,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107381,c_42224]) ).
tcf(c_108820,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_12701]) ).
tcf(c_108821,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_10144]) ).
tcf(c_108822,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107381,c_4468]) ).
tcf(c_108872,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107385,c_70]) ).
tcf(c_108873,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_69]) ).
tcf(c_108876,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_12335]) ).
tcf(c_108877,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_8396]) ).
tcf(c_108878,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_8395]) ).
tcf(c_108879,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_4044]) ).
tcf(c_108880,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107385,c_42224]) ).
tcf(c_108881,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_12701]) ).
tcf(c_108882,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_10144]) ).
tcf(c_108883,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107385,c_4468]) ).
tcf(c_108934,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK7(sK1,sK22(sK1,sK1)) = apply(sK1,empty_set) )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31401,c_52427]) ).
tcf(c_108935,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31401,c_19430]) ).
tcf(c_108936,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31401,c_4045]) ).
tcf(c_108937,plain,
( element(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31401,c_19431]) ).
tcf(c_108938,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31401,c_18734]) ).
tcf(c_108939,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31401,c_87]) ).
tcf(c_108963,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_108939,c_62,c_61]) ).
tcf(c_109007,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_37929]) ).
tcf(c_109008,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_37929]) ).
tcf(c_109009,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_37929]) ).
tcf(c_109010,plain,
relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_37929]) ).
tcf(c_109011,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_37929]) ).
tcf(c_109012,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_37929]) ).
tcf(c_109013,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_37929]) ).
tcf(c_109014,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_37929]) ).
tcf(c_109015,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_37929]) ).
tcf(c_109016,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_37929]) ).
tcf(c_109017,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_37929]) ).
tcf(c_109018,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_37929]) ).
tcf(c_109019,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_37929]) ).
tcf(c_109020,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_37929]) ).
tcf(c_109021,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_37929]) ).
tcf(c_109022,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_37929]) ).
tcf(c_109023,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_37929]) ).
tcf(c_109024,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_37929]) ).
tcf(c_109079,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38121]) ).
tcf(c_109080,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38121]) ).
tcf(c_109081,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38121]) ).
tcf(c_109082,plain,
relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38121]) ).
tcf(c_109083,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38121]) ).
tcf(c_109084,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38121]) ).
tcf(c_109085,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38121]) ).
tcf(c_109086,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38121]) ).
tcf(c_109087,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38121]) ).
tcf(c_109088,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38121]) ).
tcf(c_109089,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38121]) ).
tcf(c_109090,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38121]) ).
tcf(c_109091,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38121]) ).
tcf(c_109092,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38121]) ).
tcf(c_109093,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38121]) ).
tcf(c_109094,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38121]) ).
tcf(c_109095,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38121]) ).
tcf(c_109096,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38121]) ).
tcf(c_109151,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38122]) ).
tcf(c_109152,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38122]) ).
tcf(c_109153,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38122]) ).
tcf(c_109154,plain,
relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38122]) ).
tcf(c_109155,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38122]) ).
tcf(c_109156,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38122]) ).
tcf(c_109157,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38122]) ).
tcf(c_109158,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38122]) ).
tcf(c_109159,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38122]) ).
tcf(c_109160,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38122]) ).
tcf(c_109161,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38122]) ).
tcf(c_109162,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38122]) ).
tcf(c_109163,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38122]) ).
tcf(c_109164,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38122]) ).
tcf(c_109165,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38122]) ).
tcf(c_109166,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38122]) ).
tcf(c_109167,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38122]) ).
tcf(c_109168,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38122]) ).
tcf(c_109348,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38123]) ).
tcf(c_109349,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38123]) ).
tcf(c_109350,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38123]) ).
tcf(c_109351,plain,
relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38123]) ).
tcf(c_109352,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38123]) ).
tcf(c_109353,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38123]) ).
tcf(c_109354,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38123]) ).
tcf(c_109355,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38123]) ).
tcf(c_109356,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38123]) ).
tcf(c_109357,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38123]) ).
tcf(c_109358,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38123]) ).
tcf(c_109359,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38123]) ).
tcf(c_109360,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38123]) ).
tcf(c_109361,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38123]) ).
tcf(c_109362,plain,
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38123]) ).
tcf(c_109363,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38123]) ).
tcf(c_109364,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38123]) ).
tcf(c_109365,plain,
! [X0: $i] :
( ( relation_dom(relation_rng(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38123]) ).
tcf(c_109407,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18064]) ).
tcf(c_109408,plain,
relation_dom(relation_inverse(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18064]) ).
tcf(c_109411,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18064]) ).
tcf(c_109412,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18064]) ).
tcf(c_109413,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18064]) ).
tcf(c_109414,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18064]) ).
tcf(c_109415,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18064]) ).
tcf(c_109416,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18064]) ).
tcf(c_109417,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18064]) ).
tcf(c_109418,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18064]) ).
tcf(c_109419,plain,
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18064]) ).
tcf(c_109420,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18064]) ).
tcf(c_109422,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18064]) ).
tcf(c_109668,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18894]) ).
tcf(c_109669,plain,
relation_rng(relation_dom(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18894]) ).
tcf(c_109672,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18894]) ).
tcf(c_109673,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18894]) ).
tcf(c_109674,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18894]) ).
tcf(c_109675,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18894]) ).
tcf(c_109676,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18894]) ).
tcf(c_109677,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18894]) ).
tcf(c_109678,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18894]) ).
tcf(c_109679,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18894]) ).
tcf(c_109680,plain,
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18894]) ).
tcf(c_109681,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18894]) ).
tcf(c_109683,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18894]) ).
tcf(c_109715,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18940]) ).
tcf(c_109716,plain,
relation_rng(relation_dom(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18940]) ).
tcf(c_109719,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18940]) ).
tcf(c_109720,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18940]) ).
tcf(c_109721,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18940]) ).
tcf(c_109722,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18940]) ).
tcf(c_109723,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18940]) ).
tcf(c_109724,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18940]) ).
tcf(c_109725,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18940]) ).
tcf(c_109726,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18940]) ).
tcf(c_109727,plain,
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18940]) ).
tcf(c_109728,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18940]) ).
tcf(c_109730,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18940]) ).
tcf(c_109845,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_18993]) ).
tcf(c_109846,plain,
relation_rng(relation_dom(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_18993]) ).
tcf(c_109849,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_18993]) ).
tcf(c_109850,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_18993]) ).
tcf(c_109851,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_18993]) ).
tcf(c_109852,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_18993]) ).
tcf(c_109853,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_18993]) ).
tcf(c_109854,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_18993]) ).
tcf(c_109855,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_18993]) ).
tcf(c_109856,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_18993]) ).
tcf(c_109857,plain,
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_18993]) ).
tcf(c_109858,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_18993]) ).
tcf(c_109860,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_18993]) ).
tcf(c_109892,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107389,c_70]) ).
tcf(c_109893,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_69]) ).
tcf(c_109896,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_12335]) ).
tcf(c_109897,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_8396]) ).
tcf(c_109898,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_8395]) ).
tcf(c_109899,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_4044]) ).
tcf(c_109900,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107389,c_42224]) ).
tcf(c_109901,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_12701]) ).
tcf(c_109902,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_10144]) ).
tcf(c_109903,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107389,c_4468]) ).
tcf(c_109953,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107393,c_70]) ).
tcf(c_109954,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_69]) ).
tcf(c_109957,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_12335]) ).
tcf(c_109958,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_8396]) ).
tcf(c_109959,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_8395]) ).
tcf(c_109960,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_4044]) ).
tcf(c_109961,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107393,c_42224]) ).
tcf(c_109962,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_12701]) ).
tcf(c_109963,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_10144]) ).
tcf(c_109964,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107393,c_4468]) ).
tcf(c_110076,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ in(sK2,ordered_pair(sK7(sK1,sK22(sK1,sK1)),empty_set)) ),
inference(superposition,[status(thm)],[c_108963,c_70]) ).
tcf(c_110077,plain,
( element(ordered_pair(sK7(sK1,sK22(sK1,sK1)),empty_set),sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108963,c_69]) ).
tcf(c_110079,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ relation(sK2)
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108963,c_106]) ).
tcf(c_110084,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_110079,c_61]) ).
tcf(c_110113,plain,
( in(empty_set,relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5329,c_110084]) ).
tcf(c_110132,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_9713,c_108201]) ).
tcf(c_110133,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK22(sK2,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_4763,c_108201]) ).
tcf(c_110137,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108201,c_87]) ).
tcf(c_110138,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108201,c_100631]) ).
tcf(c_110139,plain,
( in(ordered_pair(sK22(sK2,sK1),apply(relation_inverse(sK1),sK22(sK2,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108201,c_12604]) ).
tcf(c_110140,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108201,c_12599]) ).
tcf(c_110141,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108201,c_61586]) ).
tcf(c_110143,plain,
( in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108201,c_57811]) ).
tcf(c_110165,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_110137,c_65,c_64]) ).
tcf(c_110265,plain,
( in(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_110165]) ).
tcf(c_110266,plain,
( in(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK22(sK2,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_110165]) ).
tcf(c_110267,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_110165,c_70]) ).
tcf(c_110268,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_110165,c_69]) ).
tcf(c_110270,plain,
( in(sK22(sK2,sK1),relation_rng(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_110165,c_106]) ).
tcf(c_110276,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_110270,c_4013]) ).
tcf(c_110297,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_34013,c_108202]) ).
tcf(c_110301,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108202,c_87]) ).
tcf(c_110302,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108202,c_100631]) ).
tcf(c_110303,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_108202,c_64920]) ).
tcf(c_110304,plain,
( in(ordered_pair(sK22(sK2,sK1),sK7(relation_inverse(sK1),sK22(sK2,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108202,c_12604]) ).
tcf(c_110305,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108202,c_12599]) ).
tcf(c_110306,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108202,c_61586]) ).
tcf(c_110307,plain,
( in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108202,c_57811]) ).
tcf(c_110308,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK7(relation_inverse(sK1),sK22(sK2,sK1)) = sK15(sK1,sK22(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_108202,c_57193]) ).
tcf(c_110316,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK7(relation_inverse(sK1),sK22(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_108202,c_4791]) ).
tcf(c_110317,plain,
( ( relation_inverse(sK2) = sK1 )
| ( sK22(sK2,sK1) = empty_set )
| ( apply(sK2,sK22(sK2,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK7(relation_inverse(sK1),sK22(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_108202,c_10494]) ).
tcf(c_110341,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_110301,c_65,c_64]) ).
tcf(c_110578,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_31403,c_107]) ).
tcf(c_110579,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31403,c_4848]) ).
tcf(c_110581,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31403,c_12678]) ).
tcf(c_110583,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_31403,c_59117]) ).
tcf(c_110584,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_31403,c_58270]) ).
tcf(c_110586,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31403,c_34537]) ).
tcf(c_110587,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31403,c_14876]) ).
tcf(c_110589,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(relation_dom(sK1),sK22(sK1,sK1))
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31403,c_8391]) ).
tcf(c_110592,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31403,c_71817]) ).
tcf(c_110632,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_110578,c_4013]) ).
tcf(c_110645,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38142]) ).
tcf(c_110646,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38142]) ).
tcf(c_110647,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38142]) ).
tcf(c_110648,plain,
relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38142]) ).
tcf(c_110649,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38142]) ).
tcf(c_110650,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38142]) ).
tcf(c_110651,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38142]) ).
tcf(c_110652,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38142]) ).
tcf(c_110653,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38142]) ).
tcf(c_110654,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38142]) ).
tcf(c_110655,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38142]) ).
tcf(c_110656,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38142]) ).
tcf(c_110657,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38142]) ).
tcf(c_110658,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38142]) ).
tcf(c_110659,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38142]) ).
tcf(c_110660,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38142]) ).
tcf(c_110661,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38142]) ).
tcf(c_110662,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38142]) ).
tcf(c_110702,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38143]) ).
tcf(c_110703,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38143]) ).
tcf(c_110704,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38143]) ).
tcf(c_110705,plain,
relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38143]) ).
tcf(c_110706,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38143]) ).
tcf(c_110707,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38143]) ).
tcf(c_110708,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38143]) ).
tcf(c_110709,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38143]) ).
tcf(c_110710,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38143]) ).
tcf(c_110711,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38143]) ).
tcf(c_110712,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38143]) ).
tcf(c_110713,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38143]) ).
tcf(c_110714,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38143]) ).
tcf(c_110715,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38143]) ).
tcf(c_110716,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38143]) ).
tcf(c_110717,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38143]) ).
tcf(c_110718,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38143]) ).
tcf(c_110719,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38143]) ).
tcf(c_110759,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38144]) ).
tcf(c_110760,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38144]) ).
tcf(c_110761,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38144]) ).
tcf(c_110762,plain,
relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38144]) ).
tcf(c_110763,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38144]) ).
tcf(c_110764,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38144]) ).
tcf(c_110765,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38144]) ).
tcf(c_110766,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38144]) ).
tcf(c_110767,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38144]) ).
tcf(c_110768,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38144]) ).
tcf(c_110769,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38144]) ).
tcf(c_110770,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38144]) ).
tcf(c_110771,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38144]) ).
tcf(c_110772,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38144]) ).
tcf(c_110773,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38144]) ).
tcf(c_110774,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38144]) ).
tcf(c_110775,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38144]) ).
tcf(c_110776,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38144]) ).
tcf(c_110816,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38163]) ).
tcf(c_110817,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38163]) ).
tcf(c_110818,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38163]) ).
tcf(c_110819,plain,
relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38163]) ).
tcf(c_110820,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38163]) ).
tcf(c_110821,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38163]) ).
tcf(c_110822,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38163]) ).
tcf(c_110823,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38163]) ).
tcf(c_110824,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38163]) ).
tcf(c_110825,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38163]) ).
tcf(c_110826,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38163]) ).
tcf(c_110827,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38163]) ).
tcf(c_110828,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38163]) ).
tcf(c_110829,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38163]) ).
tcf(c_110830,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38163]) ).
tcf(c_110831,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38163]) ).
tcf(c_110832,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38163]) ).
tcf(c_110833,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38163]) ).
tcf(c_110875,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19051]) ).
tcf(c_110876,plain,
relation_rng(relation_rng(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19051]) ).
tcf(c_110879,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19051]) ).
tcf(c_110880,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19051]) ).
tcf(c_110881,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19051]) ).
tcf(c_110882,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19051]) ).
tcf(c_110883,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19051]) ).
tcf(c_110884,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19051]) ).
tcf(c_110885,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19051]) ).
tcf(c_110886,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19051]) ).
tcf(c_110887,plain,
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19051]) ).
tcf(c_110888,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19051]) ).
tcf(c_110890,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19051]) ).
tcf(c_110922,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_19630]) ).
tcf(c_110923,plain,
relation_rng(relation_rng(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_19630]) ).
tcf(c_110926,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_19630]) ).
tcf(c_110927,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_19630]) ).
tcf(c_110928,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_19630]) ).
tcf(c_110929,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_19630]) ).
tcf(c_110930,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_19630]) ).
tcf(c_110931,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_19630]) ).
tcf(c_110932,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_19630]) ).
tcf(c_110933,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_19630]) ).
tcf(c_110934,plain,
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_19630]) ).
tcf(c_110935,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_19630]) ).
tcf(c_110937,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_19630]) ).
tcf(c_111101,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20574]) ).
tcf(c_111102,plain,
relation_rng(relation_rng(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20574]) ).
tcf(c_111105,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20574]) ).
tcf(c_111106,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20574]) ).
tcf(c_111107,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20574]) ).
tcf(c_111108,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20574]) ).
tcf(c_111109,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20574]) ).
tcf(c_111110,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20574]) ).
tcf(c_111111,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20574]) ).
tcf(c_111112,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20574]) ).
tcf(c_111113,plain,
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20574]) ).
tcf(c_111114,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20574]) ).
tcf(c_111116,plain,
! [X0: $i] :
( ( relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20574]) ).
tcf(c_111148,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20740]) ).
tcf(c_111149,plain,
relation_rng(relation_inverse(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20740]) ).
tcf(c_111152,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20740]) ).
tcf(c_111153,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20740]) ).
tcf(c_111154,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20740]) ).
tcf(c_111155,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20740]) ).
tcf(c_111156,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20740]) ).
tcf(c_111157,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20740]) ).
tcf(c_111158,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20740]) ).
tcf(c_111159,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20740]) ).
tcf(c_111160,plain,
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20740]) ).
tcf(c_111161,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20740]) ).
tcf(c_111163,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20740]) ).
tcf(c_111195,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_110341]) ).
tcf(c_111196,plain,
( ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_110341,c_70]) ).
tcf(c_111197,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_110341,c_69]) ).
tcf(c_111199,plain,
( in(sK22(sK2,sK1),relation_rng(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_110341,c_106]) ).
tcf(c_111204,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = sK7(relation_inverse(sK1),sK22(sK2,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_110341,c_3784]) ).
tcf(c_111205,plain,
( in(sK22(sK2,sK1),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_111199,c_4013]) ).
tcf(c_111227,plain,
( in(ordered_pair(sK22(sK2,sK1),sK15(sK1,sK22(sK2,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK2,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_108203,c_87]) ).
tcf(c_111228,plain,
( in(sK15(sK1,sK22(sK2,sK1)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108203,c_12688]) ).
tcf(c_111229,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK22(sK2,sK1)) = empty_set )
| ~ in(relation_dom(sK2),sK22(sK2,sK1))
| ~ in(sK15(sK1,sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108203,c_13471]) ).
tcf(c_111232,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1))) ),
inference(superposition,[status(thm)],[c_108203,c_34564]) ).
tcf(c_111233,plain,
( element(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_108203,c_34565]) ).
tcf(c_111234,plain,
( in(sK15(sK1,sK22(sK2,sK1)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_108203,c_34571]) ).
tcf(c_111235,plain,
( in(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_108203,c_34529]) ).
tcf(c_111239,plain,
( in(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108203,c_4623]) ).
tcf(c_111240,plain,
( in(ordered_pair(sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_108203,c_110165]) ).
tcf(c_111241,plain,
( ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK15(sK1,sK22(sK2,sK1))) = sK22(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_108203,c_108201]) ).
tcf(c_111272,plain,
( in(ordered_pair(sK22(sK2,sK1),sK15(sK1,sK22(sK2,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_111227,c_4030]) ).
tcf(c_111273,plain,
( in(ordered_pair(sK22(sK2,sK1),sK15(sK1,sK22(sK2,sK1))),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111272,c_987,c_3611]) ).
tcf(c_111358,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_8705]) ).
tcf(c_111364,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111358,c_65,c_64]) ).
tcf(c_111374,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(relation_dom(sK2),sK20(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_111364,c_70]) ).
tcf(c_111375,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_111364,c_69]) ).
tcf(c_111378,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_111364,c_12335]) ).
tcf(c_111380,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_111364,c_8395]) ).
tcf(c_111381,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_111364,c_4044]) ).
tcf(c_111382,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_111364,c_42224]) ).
tcf(c_111407,plain,
( in(ordered_pair(sK5(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(sK5(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_31465,c_87]) ).
tcf(c_111412,plain,
( in(ordered_pair(sK5(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_111407,c_3810]) ).
tcf(c_111413,plain,
( in(ordered_pair(sK5(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111412,c_1001,c_3610]) ).
tcf(c_111437,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38164]) ).
tcf(c_111438,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38164]) ).
tcf(c_111439,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38164]) ).
tcf(c_111440,plain,
relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38164]) ).
tcf(c_111441,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38164]) ).
tcf(c_111442,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38164]) ).
tcf(c_111443,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38164]) ).
tcf(c_111444,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38164]) ).
tcf(c_111445,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38164]) ).
tcf(c_111446,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38164]) ).
tcf(c_111447,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38164]) ).
tcf(c_111448,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38164]) ).
tcf(c_111449,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38164]) ).
tcf(c_111450,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38164]) ).
tcf(c_111451,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38164]) ).
tcf(c_111452,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38164]) ).
tcf(c_111453,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38164]) ).
tcf(c_111454,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38164]) ).
tcf(c_111508,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38165]) ).
tcf(c_111509,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38165]) ).
tcf(c_111510,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38165]) ).
tcf(c_111511,plain,
relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38165]) ).
tcf(c_111512,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38165]) ).
tcf(c_111513,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38165]) ).
tcf(c_111514,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38165]) ).
tcf(c_111515,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38165]) ).
tcf(c_111516,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38165]) ).
tcf(c_111517,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38165]) ).
tcf(c_111518,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38165]) ).
tcf(c_111519,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38165]) ).
tcf(c_111520,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38165]) ).
tcf(c_111521,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38165]) ).
tcf(c_111522,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38165]) ).
tcf(c_111523,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38165]) ).
tcf(c_111524,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38165]) ).
tcf(c_111525,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38165]) ).
tcf(c_111764,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38391]) ).
tcf(c_111765,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38391]) ).
tcf(c_111766,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38391]) ).
tcf(c_111767,plain,
relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38391]) ).
tcf(c_111768,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38391]) ).
tcf(c_111769,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38391]) ).
tcf(c_111770,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38391]) ).
tcf(c_111771,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38391]) ).
tcf(c_111772,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38391]) ).
tcf(c_111773,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38391]) ).
tcf(c_111774,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38391]) ).
tcf(c_111775,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38391]) ).
tcf(c_111776,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38391]) ).
tcf(c_111777,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38391]) ).
tcf(c_111778,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38391]) ).
tcf(c_111779,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38391]) ).
tcf(c_111780,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38391]) ).
tcf(c_111781,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38391]) ).
tcf(c_111821,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38392]) ).
tcf(c_111822,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38392]) ).
tcf(c_111823,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38392]) ).
tcf(c_111824,plain,
relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38392]) ).
tcf(c_111825,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38392]) ).
tcf(c_111826,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38392]) ).
tcf(c_111827,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38392]) ).
tcf(c_111828,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38392]) ).
tcf(c_111829,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38392]) ).
tcf(c_111830,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38392]) ).
tcf(c_111831,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38392]) ).
tcf(c_111832,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38392]) ).
tcf(c_111833,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38392]) ).
tcf(c_111834,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38392]) ).
tcf(c_111835,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38392]) ).
tcf(c_111836,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38392]) ).
tcf(c_111837,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38392]) ).
tcf(c_111838,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38392]) ).
tcf(c_111925,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_20797]) ).
tcf(c_111926,plain,
relation_rng(relation_inverse(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_20797]) ).
tcf(c_111929,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_20797]) ).
tcf(c_111930,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_20797]) ).
tcf(c_111931,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_20797]) ).
tcf(c_111932,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_20797]) ).
tcf(c_111933,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_20797]) ).
tcf(c_111934,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_20797]) ).
tcf(c_111935,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_20797]) ).
tcf(c_111936,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_20797]) ).
tcf(c_111937,plain,
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_20797]) ).
tcf(c_111938,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_20797]) ).
tcf(c_111940,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_20797]) ).
tcf(c_111972,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_21086]) ).
tcf(c_111973,plain,
relation_rng(relation_inverse(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_21086]) ).
tcf(c_111976,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_21086]) ).
tcf(c_111977,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_21086]) ).
tcf(c_111978,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_21086]) ).
tcf(c_111979,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_21086]) ).
tcf(c_111980,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_21086]) ).
tcf(c_111981,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_21086]) ).
tcf(c_111982,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_21086]) ).
tcf(c_111983,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_21086]) ).
tcf(c_111984,plain,
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_21086]) ).
tcf(c_111985,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_21086]) ).
tcf(c_111987,plain,
! [X0: $i] :
( ( relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_21086]) ).
tcf(c_112167,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_22312]) ).
tcf(c_112168,plain,
relation_inverse(relation_dom(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_22312]) ).
tcf(c_112171,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_22312]) ).
tcf(c_112172,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_22312]) ).
tcf(c_112173,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_22312]) ).
tcf(c_112174,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_22312]) ).
tcf(c_112175,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_22312]) ).
tcf(c_112176,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_22312]) ).
tcf(c_112177,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_22312]) ).
tcf(c_112178,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_22312]) ).
tcf(c_112179,plain,
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_22312]) ).
tcf(c_112180,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_22312]) ).
tcf(c_112182,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_22312]) ).
tcf(c_112223,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_9068]) ).
tcf(c_112224,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_9068]) ).
tcf(c_112225,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK21(relation_inverse(sK9),sK1),relation_dom(sK1))
| ( relation_inverse(relation_inverse(sK9)) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_9068]) ).
tcf(c_112226,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK21(relation_inverse(sK10),sK1),relation_dom(sK1))
| ( relation_inverse(relation_inverse(sK10)) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_9068]) ).
tcf(c_112228,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK21(X0,sK1)) ),
inference(superposition,[status(thm)],[c_9068,c_70]) ).
tcf(c_112229,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| element(sK21(X0,sK1),relation_rng(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9068,c_69]) ).
tcf(c_112230,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_9068,c_67]) ).
tcf(c_112231,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK21(sK2,sK1))) = sK21(sK2,sK1) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_9068,c_43161]) ).
tcf(c_112232,plain,
( in(sK21(sK9,sK1),relation_dom(sK1))
| ( relation_inverse(sK9) = sK1 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_9068,c_29938]) ).
tcf(c_112233,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_9068,c_69454]) ).
tcf(c_112235,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112233,c_95]) ).
tcf(c_112239,plain,
( in(sK21(sK9,sK1),relation_dom(sK1))
| ( relation_inverse(sK9) = sK1 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112232,c_83]) ).
tcf(c_112255,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK10))
| in(sK21(relation_inverse(sK10),sK1),relation_dom(sK1))
| ( sK1 = sK10 )
| ~ relation(relation_inverse(sK10)) ),
inference(light_normalisation,[status(thm)],[c_112226,c_3628]) ).
tcf(c_112260,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK9))
| in(sK21(relation_inverse(sK9),sK1),relation_dom(sK1))
| ( sK1 = sK9 )
| ~ relation(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_112225,c_3627]) ).
tcf(c_112265,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK2))
| in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_112224,c_3624]) ).
tcf(c_112270,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_112223,c_3629]) ).
tcf(c_112271,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK12))
| in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112270,c_3610]) ).
tcf(c_112289,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( relation_inverse(relation_inverse(sK2)) = sK1 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_9069]) ).
tcf(c_112290,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( relation_inverse(relation_inverse(sK9)) = sK1 )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_9069]) ).
tcf(c_112291,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( relation_inverse(relation_inverse(sK10)) = sK1 )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_9069]) ).
tcf(c_112292,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( relation_inverse(relation_inverse(sK12)) = sK1 )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_9069]) ).
tcf(c_112293,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(sK1),sK21(X0,sK1)) ),
inference(superposition,[status(thm)],[c_9069,c_70]) ).
tcf(c_112294,plain,
! [X0: $i] :
( element(sK21(X0,sK1),relation_dom(sK1))
| in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_69]) ).
tcf(c_112297,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1)))) = apply(sK1,sK21(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_12766]) ).
tcf(c_112298,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1)))) = sK7(sK1,sK21(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_12765]) ).
tcf(c_112299,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(X0,sK1)))) = apply(sK1,sK21(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_10203]) ).
tcf(c_112300,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1)))) = sK7(sK1,sK21(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_10202]) ).
tcf(c_112301,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1))) = sK15(sK1,apply(sK1,sK21(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_6249]) ).
tcf(c_112302,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1))) = sK15(sK1,sK7(sK1,sK21(X0,sK1))) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_5349]) ).
tcf(c_112304,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(X0,sK1)) = apply(sK1,sK21(X0,sK1)) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_12284]) ).
tcf(c_112305,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_4619]) ).
tcf(c_112306,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_4406]) ).
tcf(c_112307,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK22(X0,sK1)) ),
inference(superposition,[status(thm)],[c_9069,c_70]) ).
tcf(c_112308,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| element(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_69]) ).
tcf(c_112309,plain,
! [X0: $i] :
( in(sK21(X0,sK1),relation_dom(sK1))
| ( relation_inverse(X0) = sK1 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_9069,c_67]) ).
tcf(c_112311,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_12766]) ).
tcf(c_112312,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_12765]) ).
tcf(c_112313,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_10203]) ).
tcf(c_112314,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_10202]) ).
tcf(c_112315,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_6249]) ).
tcf(c_112316,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_5349]) ).
tcf(c_112318,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_12284]) ).
tcf(c_112319,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_4619]) ).
tcf(c_112320,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_4406]) ).
tcf(c_112325,plain,
( in(sK21(sK2,sK1),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK2,sK1)) = apply(sK2,sK22(sK2,sK1)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_9069,c_42224]) ).
tcf(c_112329,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_9069,c_68472]) ).
tcf(c_112332,plain,
( in(sK21(sK12,sK1),relation_dom(sK1))
| ( relation_inverse(sK12) = sK1 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112329,c_95]) ).
tcf(c_112356,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( sK1 = sK12 )
| ~ relation(relation_inverse(sK12)) ),
inference(light_normalisation,[status(thm)],[c_112292,c_3629]) ).
tcf(c_112357,plain,
( in(sK21(relation_inverse(sK12),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK12),sK1),relation_rng(sK12))
| ( sK1 = sK12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112356,c_3610]) ).
tcf(c_112361,plain,
( in(sK21(relation_inverse(sK10),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK10),sK1),relation_rng(sK10))
| ( sK1 = sK10 )
| ~ relation(relation_inverse(sK10)) ),
inference(light_normalisation,[status(thm)],[c_112291,c_3628]) ).
tcf(c_112366,plain,
( in(sK21(relation_inverse(sK9),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK9),sK1),relation_rng(sK9))
| ( sK1 = sK9 )
| ~ relation(relation_inverse(sK9)) ),
inference(light_normalisation,[status(thm)],[c_112290,c_3627]) ).
tcf(c_112371,plain,
( in(sK21(relation_inverse(sK2),sK1),relation_dom(sK1))
| in(sK22(relation_inverse(sK2),sK1),relation_rng(sK2))
| ( sK1 = sK2 )
| ~ relation(relation_inverse(sK2)) ),
inference(light_normalisation,[status(thm)],[c_112289,c_3624]) ).
tcf(c_112376,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112320,c_64]) ).
tcf(c_112380,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112319,c_64]) ).
tcf(c_112384,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112318,c_64]) ).
tcf(c_112406,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112316,c_64]) ).
tcf(c_112410,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112315,c_64]) ).
tcf(c_112414,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112314,c_64]) ).
tcf(c_112418,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112313,c_64]) ).
tcf(c_112422,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112312,c_64]) ).
tcf(c_112426,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112311,c_64]) ).
tcf(c_112467,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112376,c_70]) ).
tcf(c_112468,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_69]) ).
tcf(c_112471,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112376,c_12766]) ).
tcf(c_112472,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112376,c_12765]) ).
tcf(c_112473,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112376,c_10203]) ).
tcf(c_112474,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112376,c_10202]) ).
tcf(c_112475,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112376,c_6249]) ).
tcf(c_112476,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_5349]) ).
tcf(c_112478,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_12284]) ).
tcf(c_112479,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_4619]) ).
tcf(c_112480,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_4406]) ).
tcf(c_112524,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112380,c_70]) ).
tcf(c_112525,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_69]) ).
tcf(c_112528,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112380,c_12766]) ).
tcf(c_112529,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112380,c_12765]) ).
tcf(c_112530,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112380,c_10203]) ).
tcf(c_112531,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112380,c_10202]) ).
tcf(c_112532,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_6249]) ).
tcf(c_112533,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_5349]) ).
tcf(c_112535,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_12284]) ).
tcf(c_112536,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_4619]) ).
tcf(c_112537,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_4406]) ).
tcf(c_112581,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112384,c_70]) ).
tcf(c_112582,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_69]) ).
tcf(c_112585,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_12766]) ).
tcf(c_112586,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_12765]) ).
tcf(c_112587,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_10203]) ).
tcf(c_112588,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_10202]) ).
tcf(c_112589,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112384,c_6249]) ).
tcf(c_112590,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112384,c_5349]) ).
tcf(c_112592,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112384,c_12284]) ).
tcf(c_112593,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112384,c_4619]) ).
tcf(c_112594,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112384,c_4406]) ).
tcf(c_112839,plain,
( in(ordered_pair(sK13(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(sK13(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12))) ),
inference(superposition,[status(thm)],[c_31466,c_87]) ).
tcf(c_112844,plain,
( in(ordered_pair(sK13(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ function(relation_inverse(sK12))
| ~ relation(relation_inverse(sK12))
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(light_normalisation,[status(thm)],[c_112839,c_3810]) ).
tcf(c_112845,plain,
( in(ordered_pair(sK13(sK1,relation_rng(sK12)),empty_set),relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112844,c_1001,c_3610]) ).
tcf(c_112869,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38393]) ).
tcf(c_112870,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38393]) ).
tcf(c_112871,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38393]) ).
tcf(c_112872,plain,
relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38393]) ).
tcf(c_112873,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38393]) ).
tcf(c_112874,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38393]) ).
tcf(c_112875,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38393]) ).
tcf(c_112876,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38393]) ).
tcf(c_112877,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38393]) ).
tcf(c_112878,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38393]) ).
tcf(c_112879,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38393]) ).
tcf(c_112880,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38393]) ).
tcf(c_112881,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38393]) ).
tcf(c_112882,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38393]) ).
tcf(c_112883,plain,
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38393]) ).
tcf(c_112884,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38393]) ).
tcf(c_112885,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38393]) ).
tcf(c_112886,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_dom(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38393]) ).
tcf(c_112951,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38412]) ).
tcf(c_112952,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38412]) ).
tcf(c_112953,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38412]) ).
tcf(c_112954,plain,
relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38412]) ).
tcf(c_112955,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38412]) ).
tcf(c_112956,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38412]) ).
tcf(c_112957,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38412]) ).
tcf(c_112958,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38412]) ).
tcf(c_112959,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38412]) ).
tcf(c_112960,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38412]) ).
tcf(c_112961,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38412]) ).
tcf(c_112962,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38412]) ).
tcf(c_112963,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38412]) ).
tcf(c_112964,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38412]) ).
tcf(c_112965,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38412]) ).
tcf(c_112966,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38412]) ).
tcf(c_112967,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38412]) ).
tcf(c_112968,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38412]) ).
tcf(c_113036,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38413]) ).
tcf(c_113037,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38413]) ).
tcf(c_113038,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38413]) ).
tcf(c_113039,plain,
relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38413]) ).
tcf(c_113040,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38413]) ).
tcf(c_113041,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38413]) ).
tcf(c_113042,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38413]) ).
tcf(c_113043,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38413]) ).
tcf(c_113044,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38413]) ).
tcf(c_113045,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38413]) ).
tcf(c_113046,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38413]) ).
tcf(c_113047,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38413]) ).
tcf(c_113048,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38413]) ).
tcf(c_113049,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38413]) ).
tcf(c_113050,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38413]) ).
tcf(c_113051,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38413]) ).
tcf(c_113052,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38413]) ).
tcf(c_113053,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38413]) ).
tcf(c_113093,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38414]) ).
tcf(c_113094,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38414]) ).
tcf(c_113095,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38414]) ).
tcf(c_113096,plain,
relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38414]) ).
tcf(c_113097,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38414]) ).
tcf(c_113098,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38414]) ).
tcf(c_113099,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38414]) ).
tcf(c_113100,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38414]) ).
tcf(c_113101,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38414]) ).
tcf(c_113102,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38414]) ).
tcf(c_113103,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38414]) ).
tcf(c_113104,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38414]) ).
tcf(c_113105,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38414]) ).
tcf(c_113106,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38414]) ).
tcf(c_113107,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38414]) ).
tcf(c_113108,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38414]) ).
tcf(c_113109,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38414]) ).
tcf(c_113110,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38414]) ).
tcf(c_113173,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23378]) ).
tcf(c_113174,plain,
relation_inverse(relation_dom(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23378]) ).
tcf(c_113177,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23378]) ).
tcf(c_113178,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23378]) ).
tcf(c_113179,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23378]) ).
tcf(c_113180,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23378]) ).
tcf(c_113181,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23378]) ).
tcf(c_113182,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23378]) ).
tcf(c_113183,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23378]) ).
tcf(c_113184,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23378]) ).
tcf(c_113185,plain,
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23378]) ).
tcf(c_113186,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23378]) ).
tcf(c_113188,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23378]) ).
tcf(c_113282,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23413]) ).
tcf(c_113283,plain,
relation_inverse(relation_dom(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23413]) ).
tcf(c_113286,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23413]) ).
tcf(c_113287,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23413]) ).
tcf(c_113288,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23413]) ).
tcf(c_113289,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23413]) ).
tcf(c_113290,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23413]) ).
tcf(c_113291,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23413]) ).
tcf(c_113292,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23413]) ).
tcf(c_113293,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23413]) ).
tcf(c_113294,plain,
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23413]) ).
tcf(c_113295,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23413]) ).
tcf(c_113297,plain,
! [X0: $i] :
( ( relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23413]) ).
tcf(c_113329,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23527]) ).
tcf(c_113330,plain,
relation_inverse(relation_rng(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23527]) ).
tcf(c_113333,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23527]) ).
tcf(c_113334,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23527]) ).
tcf(c_113335,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23527]) ).
tcf(c_113336,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23527]) ).
tcf(c_113337,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23527]) ).
tcf(c_113338,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23527]) ).
tcf(c_113339,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23527]) ).
tcf(c_113340,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23527]) ).
tcf(c_113341,plain,
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23527]) ).
tcf(c_113342,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23527]) ).
tcf(c_113344,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23527]) ).
tcf(c_113609,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112406,c_70]) ).
tcf(c_113610,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_69]) ).
tcf(c_113613,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112406,c_12766]) ).
tcf(c_113614,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112406,c_12765]) ).
tcf(c_113615,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112406,c_10203]) ).
tcf(c_113616,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112406,c_10202]) ).
tcf(c_113617,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_6249]) ).
tcf(c_113618,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_5349]) ).
tcf(c_113620,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_12284]) ).
tcf(c_113621,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112406,c_4619]) ).
tcf(c_113622,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_4406]) ).
tcf(c_113666,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112410,c_70]) ).
tcf(c_113667,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_69]) ).
tcf(c_113670,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112410,c_12766]) ).
tcf(c_113671,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112410,c_12765]) ).
tcf(c_113672,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112410,c_10203]) ).
tcf(c_113673,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112410,c_10202]) ).
tcf(c_113674,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_6249]) ).
tcf(c_113675,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_5349]) ).
tcf(c_113677,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_12284]) ).
tcf(c_113678,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_4619]) ).
tcf(c_113679,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_4406]) ).
tcf(c_113723,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112414,c_70]) ).
tcf(c_113724,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_69]) ).
tcf(c_113727,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_12766]) ).
tcf(c_113728,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_12765]) ).
tcf(c_113729,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_10203]) ).
tcf(c_113730,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_10202]) ).
tcf(c_113731,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_6249]) ).
tcf(c_113732,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_5349]) ).
tcf(c_113734,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_12284]) ).
tcf(c_113735,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_4619]) ).
tcf(c_113736,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_4406]) ).
tcf(c_113780,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112418,c_70]) ).
tcf(c_113781,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_69]) ).
tcf(c_113784,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_12766]) ).
tcf(c_113785,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_12765]) ).
tcf(c_113786,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_10203]) ).
tcf(c_113787,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_10202]) ).
tcf(c_113788,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_6249]) ).
tcf(c_113789,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_5349]) ).
tcf(c_113791,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_12284]) ).
tcf(c_113792,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_4619]) ).
tcf(c_113793,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_4406]) ).
tcf(c_113837,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112422,c_70]) ).
tcf(c_113838,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_69]) ).
tcf(c_113841,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_12766]) ).
tcf(c_113842,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_12765]) ).
tcf(c_113843,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_10203]) ).
tcf(c_113844,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_10202]) ).
tcf(c_113845,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_6249]) ).
tcf(c_113846,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_5349]) ).
tcf(c_113848,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_12284]) ).
tcf(c_113849,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_4619]) ).
tcf(c_113850,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_4406]) ).
tcf(c_114005,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112426,c_70]) ).
tcf(c_114006,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_69]) ).
tcf(c_114009,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_12766]) ).
tcf(c_114010,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_12765]) ).
tcf(c_114011,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_10203]) ).
tcf(c_114012,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_10202]) ).
tcf(c_114013,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_6249]) ).
tcf(c_114014,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_5349]) ).
tcf(c_114016,plain,
( ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_12284]) ).
tcf(c_114017,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_4619]) ).
tcf(c_114018,plain,
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_4406]) ).
tcf(c_114067,plain,
( in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3820,c_9230]) ).
tcf(c_114068,plain,
( in(sK22(sK1,relation_inverse(sK2)),relation_dom(sK2))
| in(sK22(sK1,relation_inverse(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3845,c_9230]) ).
tcf(c_114069,plain,
( in(sK22(sK1,relation_inverse(sK9)),relation_dom(sK9))
| in(sK22(sK1,relation_inverse(sK9)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK9) )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3848,c_9230]) ).
tcf(c_114070,plain,
( in(sK22(sK1,relation_inverse(sK10)),relation_dom(sK10))
| in(sK22(sK1,relation_inverse(sK10)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK10) )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3849,c_9230]) ).
tcf(c_114072,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_rng(X0),sK22(sK1,X0)) ),
inference(superposition,[status(thm)],[c_9230,c_70]) ).
tcf(c_114073,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| element(sK22(sK1,X0),relation_rng(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9230,c_69]) ).
tcf(c_114074,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_9230,c_67]) ).
tcf(c_114075,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,sK2))) = sK22(sK1,sK2) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_9230,c_43161]) ).
tcf(c_114076,plain,
( in(sK22(sK1,sK9),relation_dom(sK1))
| ( relation_inverse(sK1) = sK9 )
| ~ relation(sK9)
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_9230,c_29938]) ).
tcf(c_114077,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_9230,c_69454]) ).
tcf(c_114079,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_dom(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114077,c_95]) ).
tcf(c_114083,plain,
( in(sK22(sK1,sK9),relation_dom(sK1))
| ( relation_inverse(sK1) = sK9 )
| ~ empty(relation_inverse(sK9)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114076,c_83]) ).
tcf(c_114111,plain,
( in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK12))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114067,c_3610]) ).
tcf(c_114308,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38433]) ).
tcf(c_114309,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38433]) ).
tcf(c_114310,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38433]) ).
tcf(c_114311,plain,
relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38433]) ).
tcf(c_114312,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38433]) ).
tcf(c_114313,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38433]) ).
tcf(c_114314,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38433]) ).
tcf(c_114315,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38433]) ).
tcf(c_114316,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38433]) ).
tcf(c_114317,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38433]) ).
tcf(c_114318,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38433]) ).
tcf(c_114319,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38433]) ).
tcf(c_114320,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38433]) ).
tcf(c_114321,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38433]) ).
tcf(c_114322,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38433]) ).
tcf(c_114323,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38433]) ).
tcf(c_114324,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38433]) ).
tcf(c_114325,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38433]) ).
tcf(c_114365,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38434]) ).
tcf(c_114366,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38434]) ).
tcf(c_114367,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38434]) ).
tcf(c_114368,plain,
relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38434]) ).
tcf(c_114369,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38434]) ).
tcf(c_114370,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38434]) ).
tcf(c_114371,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38434]) ).
tcf(c_114372,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38434]) ).
tcf(c_114373,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38434]) ).
tcf(c_114374,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38434]) ).
tcf(c_114375,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38434]) ).
tcf(c_114376,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38434]) ).
tcf(c_114377,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38434]) ).
tcf(c_114378,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38434]) ).
tcf(c_114379,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38434]) ).
tcf(c_114380,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38434]) ).
tcf(c_114381,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38434]) ).
tcf(c_114382,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38434]) ).
tcf(c_114422,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38435]) ).
tcf(c_114423,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38435]) ).
tcf(c_114424,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38435]) ).
tcf(c_114425,plain,
relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38435]) ).
tcf(c_114426,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38435]) ).
tcf(c_114427,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38435]) ).
tcf(c_114428,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38435]) ).
tcf(c_114429,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38435]) ).
tcf(c_114430,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38435]) ).
tcf(c_114431,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38435]) ).
tcf(c_114432,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38435]) ).
tcf(c_114433,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38435]) ).
tcf(c_114434,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38435]) ).
tcf(c_114435,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38435]) ).
tcf(c_114436,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38435]) ).
tcf(c_114437,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38435]) ).
tcf(c_114438,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38435]) ).
tcf(c_114439,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38435]) ).
tcf(c_114479,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38454]) ).
tcf(c_114480,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38454]) ).
tcf(c_114481,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38454]) ).
tcf(c_114482,plain,
relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38454]) ).
tcf(c_114483,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38454]) ).
tcf(c_114484,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38454]) ).
tcf(c_114485,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38454]) ).
tcf(c_114486,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38454]) ).
tcf(c_114487,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38454]) ).
tcf(c_114488,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38454]) ).
tcf(c_114489,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38454]) ).
tcf(c_114490,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38454]) ).
tcf(c_114491,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38454]) ).
tcf(c_114492,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38454]) ).
tcf(c_114493,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38454]) ).
tcf(c_114494,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38454]) ).
tcf(c_114495,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38454]) ).
tcf(c_114496,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38454]) ).
tcf(c_114538,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_23564]) ).
tcf(c_114539,plain,
relation_inverse(relation_rng(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_23564]) ).
tcf(c_114542,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_23564]) ).
tcf(c_114543,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_23564]) ).
tcf(c_114544,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_23564]) ).
tcf(c_114545,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_23564]) ).
tcf(c_114546,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_23564]) ).
tcf(c_114547,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_23564]) ).
tcf(c_114548,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_23564]) ).
tcf(c_114549,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_23564]) ).
tcf(c_114550,plain,
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_23564]) ).
tcf(c_114551,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_23564]) ).
tcf(c_114553,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_23564]) ).
tcf(c_114812,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24306]) ).
tcf(c_114813,plain,
relation_inverse(relation_rng(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24306]) ).
tcf(c_114816,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24306]) ).
tcf(c_114817,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24306]) ).
tcf(c_114818,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24306]) ).
tcf(c_114819,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24306]) ).
tcf(c_114820,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24306]) ).
tcf(c_114821,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24306]) ).
tcf(c_114822,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24306]) ).
tcf(c_114823,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24306]) ).
tcf(c_114824,plain,
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24306]) ).
tcf(c_114825,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24306]) ).
tcf(c_114827,plain,
! [X0: $i] :
( ( relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24306]) ).
tcf(c_114859,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24368]) ).
tcf(c_114860,plain,
relation_inverse(relation_inverse(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24368]) ).
tcf(c_114863,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24368]) ).
tcf(c_114864,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24368]) ).
tcf(c_114865,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24368]) ).
tcf(c_114866,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24368]) ).
tcf(c_114867,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24368]) ).
tcf(c_114868,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24368]) ).
tcf(c_114869,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24368]) ).
tcf(c_114870,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24368]) ).
tcf(c_114871,plain,
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24368]) ).
tcf(c_114872,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24368]) ).
tcf(c_114874,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24368]) ).
tcf(c_114933,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24405]) ).
tcf(c_114934,plain,
relation_inverse(relation_inverse(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24405]) ).
tcf(c_114937,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24405]) ).
tcf(c_114938,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24405]) ).
tcf(c_114939,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24405]) ).
tcf(c_114940,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24405]) ).
tcf(c_114941,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24405]) ).
tcf(c_114942,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24405]) ).
tcf(c_114943,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24405]) ).
tcf(c_114944,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24405]) ).
tcf(c_114945,plain,
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24405]) ).
tcf(c_114946,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24405]) ).
tcf(c_114948,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24405]) ).
tcf(c_114984,plain,
( in(sK21(sK1,relation_inverse(sK2)),relation_rng(sK2))
| in(sK22(sK1,relation_inverse(sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK2) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_3805,c_9231]) ).
tcf(c_114985,plain,
( in(sK21(sK1,relation_inverse(sK9)),relation_rng(sK9))
| in(sK22(sK1,relation_inverse(sK9)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK9) )
| ~ relation(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_3808,c_9231]) ).
tcf(c_114986,plain,
( in(sK21(sK1,relation_inverse(sK10)),relation_rng(sK10))
| in(sK22(sK1,relation_inverse(sK10)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK10) )
| ~ relation(relation_inverse(sK10)) ),
inference(superposition,[status(thm)],[c_3809,c_9231]) ).
tcf(c_114987,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_rng(sK12))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK12) )
| ~ relation(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_3810,c_9231]) ).
tcf(c_114988,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ in(relation_dom(X0),sK21(sK1,X0)) ),
inference(superposition,[status(thm)],[c_9231,c_70]) ).
tcf(c_114989,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| element(sK21(sK1,X0),relation_dom(X0))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9231,c_69]) ).
tcf(c_114990,plain,
! [X0: $i] :
( in(sK22(sK1,X0),relation_dom(sK1))
| ( relation_inverse(sK1) = X0 )
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(superposition,[status(thm)],[c_9231,c_67]) ).
tcf(c_115006,plain,
( in(sK22(sK1,sK2),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ~ relation(sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_9231,c_42224]) ).
tcf(c_115010,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ relation(sK12)
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_9231,c_68472]) ).
tcf(c_115013,plain,
( in(sK22(sK1,sK12),relation_dom(sK1))
| ( relation_inverse(sK1) = sK12 )
| ~ empty(relation_rng(sK12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_115010,c_95]) ).
tcf(c_115029,plain,
( in(sK21(sK1,relation_inverse(sK12)),relation_rng(sK12))
| in(sK22(sK1,relation_inverse(sK12)),relation_dom(sK1))
| ( relation_inverse(sK1) = relation_inverse(sK12) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_114987,c_3610]) ).
tcf(c_115131,plain,
! [X0: $i] :
( ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(X0,sK13(sK1,relation_dom(X0))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(X0))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_10569]) ).
tcf(c_115132,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_10569]) ).
tcf(c_115133,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_10569]) ).
tcf(c_115134,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_10569]) ).
tcf(c_115135,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_10569]) ).
tcf(c_115138,plain,
( ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(relation_inverse(sK2),sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = empty_set )
| ~ function(relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_4510,c_10569]) ).
tcf(c_115140,plain,
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_10569]) ).
tcf(c_115141,plain,
! [X0: $i] :
( element(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8430,c_10569]) ).
tcf(c_115142,plain,
! [X0: $i] :
( element(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_6336,c_10569]) ).
tcf(c_115143,plain,
! [X0: $i] :
( in(sK14(sK1,X0),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_8298,c_10569]) ).
tcf(c_115144,plain,
! [X0: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_5563,c_10569]) ).
tcf(c_115145,plain,
! [X0: $i] :
( in(sK13(sK1,X0),relation_dom(sK2))
| ( relation_dom(sK2) = X0 )
| ( apply(relation_inverse(sK1),sK13(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_5542,c_10569]) ).
tcf(c_115210,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38455]) ).
tcf(c_115211,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38455]) ).
tcf(c_115212,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38455]) ).
tcf(c_115213,plain,
relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38455]) ).
tcf(c_115214,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38455]) ).
tcf(c_115215,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38455]) ).
tcf(c_115216,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38455]) ).
tcf(c_115217,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38455]) ).
tcf(c_115218,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38455]) ).
tcf(c_115219,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38455]) ).
tcf(c_115220,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38455]) ).
tcf(c_115221,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38455]) ).
tcf(c_115222,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38455]) ).
tcf(c_115223,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38455]) ).
tcf(c_115224,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38455]) ).
tcf(c_115225,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38455]) ).
tcf(c_115226,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38455]) ).
tcf(c_115227,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38455]) ).
tcf(c_115317,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38456]) ).
tcf(c_115318,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38456]) ).
tcf(c_115319,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38456]) ).
tcf(c_115320,plain,
relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38456]) ).
tcf(c_115321,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38456]) ).
tcf(c_115322,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38456]) ).
tcf(c_115323,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38456]) ).
tcf(c_115324,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38456]) ).
tcf(c_115325,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38456]) ).
tcf(c_115326,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38456]) ).
tcf(c_115327,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38456]) ).
tcf(c_115328,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38456]) ).
tcf(c_115329,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38456]) ).
tcf(c_115330,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38456]) ).
tcf(c_115331,plain,
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38456]) ).
tcf(c_115332,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38456]) ).
tcf(c_115333,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38456]) ).
tcf(c_115334,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_rng(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38456]) ).
tcf(c_115374,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38694]) ).
tcf(c_115375,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38694]) ).
tcf(c_115376,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38694]) ).
tcf(c_115377,plain,
relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38694]) ).
tcf(c_115378,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38694]) ).
tcf(c_115379,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38694]) ).
tcf(c_115380,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38694]) ).
tcf(c_115381,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38694]) ).
tcf(c_115382,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38694]) ).
tcf(c_115383,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38694]) ).
tcf(c_115384,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38694]) ).
tcf(c_115385,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38694]) ).
tcf(c_115386,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38694]) ).
tcf(c_115387,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38694]) ).
tcf(c_115388,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38694]) ).
tcf(c_115389,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38694]) ).
tcf(c_115390,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38694]) ).
tcf(c_115391,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38694]) ).
tcf(c_115431,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38695]) ).
tcf(c_115432,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38695]) ).
tcf(c_115433,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38695]) ).
tcf(c_115434,plain,
relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38695]) ).
tcf(c_115435,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38695]) ).
tcf(c_115436,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38695]) ).
tcf(c_115437,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38695]) ).
tcf(c_115438,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38695]) ).
tcf(c_115439,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38695]) ).
tcf(c_115440,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38695]) ).
tcf(c_115441,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38695]) ).
tcf(c_115442,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38695]) ).
tcf(c_115443,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38695]) ).
tcf(c_115444,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38695]) ).
tcf(c_115445,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38695]) ).
tcf(c_115446,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38695]) ).
tcf(c_115447,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38695]) ).
tcf(c_115448,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38695]) ).
tcf(c_115688,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_24519]) ).
tcf(c_115689,plain,
relation_inverse(relation_inverse(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_24519]) ).
tcf(c_115692,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_24519]) ).
tcf(c_115693,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_24519]) ).
tcf(c_115694,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_24519]) ).
tcf(c_115695,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_24519]) ).
tcf(c_115696,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_24519]) ).
tcf(c_115697,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_24519]) ).
tcf(c_115698,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_24519]) ).
tcf(c_115699,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_24519]) ).
tcf(c_115700,plain,
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_24519]) ).
tcf(c_115701,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_24519]) ).
tcf(c_115703,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_24519]) ).
tcf(c_115735,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25255]) ).
tcf(c_115736,plain,
sK20(powerset(relation_dom(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25255]) ).
tcf(c_115739,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25255]) ).
tcf(c_115740,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25255]) ).
tcf(c_115741,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25255]) ).
tcf(c_115742,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25255]) ).
tcf(c_115743,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25255]) ).
tcf(c_115744,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25255]) ).
tcf(c_115745,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25255]) ).
tcf(c_115746,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25255]) ).
tcf(c_115747,plain,
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25255]) ).
tcf(c_115748,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25255]) ).
tcf(c_115750,plain,
! [X0: $i] :
( ( sK20(powerset(relation_dom(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25255]) ).
tcf(c_115782,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25319]) ).
tcf(c_115783,plain,
sK20(powerset(relation_rng(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25319]) ).
tcf(c_115786,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25319]) ).
tcf(c_115787,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25319]) ).
tcf(c_115788,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25319]) ).
tcf(c_115789,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25319]) ).
tcf(c_115790,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25319]) ).
tcf(c_115791,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25319]) ).
tcf(c_115792,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25319]) ).
tcf(c_115793,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25319]) ).
tcf(c_115794,plain,
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25319]) ).
tcf(c_115795,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25319]) ).
tcf(c_115797,plain,
! [X0: $i] :
( ( sK20(powerset(relation_rng(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25319]) ).
tcf(c_115829,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_25354]) ).
tcf(c_115830,plain,
sK20(powerset(relation_inverse(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_25354]) ).
tcf(c_115833,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_25354]) ).
tcf(c_115834,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_25354]) ).
tcf(c_115835,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_25354]) ).
tcf(c_115836,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_25354]) ).
tcf(c_115837,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_25354]) ).
tcf(c_115838,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_25354]) ).
tcf(c_115839,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_25354]) ).
tcf(c_115840,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_25354]) ).
tcf(c_115841,plain,
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_25354]) ).
tcf(c_115842,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_25354]) ).
tcf(c_115844,plain,
! [X0: $i] :
( ( sK20(powerset(relation_inverse(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_25354]) ).
tcf(c_115888,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64169,c_12677]) ).
tcf(c_115892,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ in(sK1,ordered_pair(X0,sK7(sK1,X0))) ),
inference(superposition,[status(thm)],[c_12677,c_70]) ).
tcf(c_115893,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12677,c_69]) ).
tcf(c_115895,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0)
| ~ in(sK7(sK1,sK5(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12677,c_76]) ).
tcf(c_115896,plain,
! [X0: $i] :
( in(sK7(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12677,c_106]) ).
tcf(c_115897,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12677,c_78]) ).
tcf(c_115921,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK2,X0),X0),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(apply(sK1,apply(sK2,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52427,c_12679]) ).
tcf(c_115922,plain,
( in(ordered_pair(apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8695,c_12679]) ).
tcf(c_115923,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12791,c_12679]) ).
tcf(c_115924,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13464,c_12679]) ).
tcf(c_115928,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10244,c_12679]) ).
tcf(c_115930,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_60275,c_12679]) ).
tcf(c_115931,plain,
! [X0: $i] :
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61136,c_12679]) ).
tcf(c_115932,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10207,c_12679]) ).
tcf(c_115933,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10226,c_12679]) ).
tcf(c_115934,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10228,c_12679]) ).
tcf(c_115936,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10231,c_12679]) ).
tcf(c_115938,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),X0),X0),sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12807,c_12679]) ).
tcf(c_115939,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_63810,c_12679]) ).
tcf(c_115940,plain,
! [X0: $i] :
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64920,c_12679]) ).
tcf(c_115941,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12770,c_12679]) ).
tcf(c_115942,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1)),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12789,c_12679]) ).
tcf(c_115943,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set)),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12794,c_12679]) ).
tcf(c_115944,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13383,c_12679]) ).
tcf(c_115945,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13385,c_12679]) ).
tcf(c_115946,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14030,c_12679]) ).
tcf(c_115947,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2))),sK1)
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14032,c_12679]) ).
tcf(c_115954,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102956,c_12679]) ).
tcf(c_115955,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102957,c_12679]) ).
tcf(c_115956,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108201,c_12679]) ).
tcf(c_115957,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1)),sK1)
| ( relation_inverse(sK2) = sK1 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108202,c_12679]) ).
tcf(c_115959,plain,
! [X0: $i] :
( in(ordered_pair(sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64168,c_12679]) ).
tcf(c_115962,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,apply(sK2,sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102954,c_12679]) ).
tcf(c_115963,plain,
! [X0: $i] :
( ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ in(sK1,ordered_pair(X0,apply(sK1,X0))) ),
inference(superposition,[status(thm)],[c_12679,c_70]) ).
tcf(c_115964,plain,
! [X0: $i] :
( element(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12679,c_69]) ).
tcf(c_115966,plain,
! [X0: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ relation(sK1)
| ~ in(sK5(sK1,X0),X0)
| ~ in(apply(sK1,sK5(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12679,c_76]) ).
tcf(c_115967,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12679,c_106]) ).
tcf(c_115968,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK1)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12679,c_78]) ).
tcf(c_116369,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38696]) ).
tcf(c_116370,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38696]) ).
tcf(c_116371,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38696]) ).
tcf(c_116372,plain,
relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38696]) ).
tcf(c_116373,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38696]) ).
tcf(c_116374,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38696]) ).
tcf(c_116375,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38696]) ).
tcf(c_116376,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38696]) ).
tcf(c_116377,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38696]) ).
tcf(c_116378,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38696]) ).
tcf(c_116379,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38696]) ).
tcf(c_116380,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38696]) ).
tcf(c_116381,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38696]) ).
tcf(c_116382,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38696]) ).
tcf(c_116383,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38696]) ).
tcf(c_116384,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38696]) ).
tcf(c_116385,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38696]) ).
tcf(c_116386,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_dom(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38696]) ).
tcf(c_116462,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38748]) ).
tcf(c_116463,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38748]) ).
tcf(c_116464,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38748]) ).
tcf(c_116465,plain,
relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38748]) ).
tcf(c_116466,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38748]) ).
tcf(c_116467,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38748]) ).
tcf(c_116468,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38748]) ).
tcf(c_116469,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38748]) ).
tcf(c_116470,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38748]) ).
tcf(c_116471,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38748]) ).
tcf(c_116472,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38748]) ).
tcf(c_116473,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38748]) ).
tcf(c_116474,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38748]) ).
tcf(c_116475,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38748]) ).
tcf(c_116476,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38748]) ).
tcf(c_116477,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38748]) ).
tcf(c_116478,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38748]) ).
tcf(c_116479,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38748]) ).
tcf(c_116560,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38749]) ).
tcf(c_116561,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38749]) ).
tcf(c_116562,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38749]) ).
tcf(c_116563,plain,
relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38749]) ).
tcf(c_116564,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38749]) ).
tcf(c_116565,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38749]) ).
tcf(c_116566,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38749]) ).
tcf(c_116567,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38749]) ).
tcf(c_116568,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38749]) ).
tcf(c_116569,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38749]) ).
tcf(c_116570,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38749]) ).
tcf(c_116571,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38749]) ).
tcf(c_116572,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38749]) ).
tcf(c_116573,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38749]) ).
tcf(c_116574,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38749]) ).
tcf(c_116575,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38749]) ).
tcf(c_116576,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38749]) ).
tcf(c_116577,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38749]) ).
tcf(c_116930,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38750]) ).
tcf(c_116931,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38750]) ).
tcf(c_116932,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38750]) ).
tcf(c_116933,plain,
relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38750]) ).
tcf(c_116934,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38750]) ).
tcf(c_116935,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38750]) ).
tcf(c_116936,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38750]) ).
tcf(c_116937,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38750]) ).
tcf(c_116938,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38750]) ).
tcf(c_116939,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38750]) ).
tcf(c_116940,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38750]) ).
tcf(c_116941,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38750]) ).
tcf(c_116942,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38750]) ).
tcf(c_116943,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38750]) ).
tcf(c_116944,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38750]) ).
tcf(c_116945,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38750]) ).
tcf(c_116946,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38750]) ).
tcf(c_116947,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_rng(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38750]) ).
tcf(c_116989,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_27408]) ).
tcf(c_116990,plain,
relation_inverse(sK20(powerset(sK20(powerset(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_27408]) ).
tcf(c_116993,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_27408]) ).
tcf(c_116994,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_27408]) ).
tcf(c_116995,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_27408]) ).
tcf(c_116996,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_27408]) ).
tcf(c_116997,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_27408]) ).
tcf(c_116998,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_27408]) ).
tcf(c_116999,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_27408]) ).
tcf(c_117000,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_27408]) ).
tcf(c_117001,plain,
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_27408]) ).
tcf(c_117002,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_27408]) ).
tcf(c_117004,plain,
! [X0: $i] :
( ( relation_inverse(sK20(powerset(sK20(powerset(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_27408]) ).
tcf(c_117042,plain,
! [X0: $i] :
( element(ordered_pair(X0,sK7(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_56204,c_14905]) ).
tcf(c_117043,plain,
! [X0: $i] :
( element(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(sK15(sK1,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57193,c_14905]) ).
tcf(c_117045,plain,
( element(ordered_pair(sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_14967,c_14905]) ).
tcf(c_117046,plain,
( element(ordered_pair(sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1)))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_15831,c_14905]) ).
tcf(c_117051,plain,
( element(ordered_pair(sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_28868,c_14905]) ).
tcf(c_117052,plain,
( element(ordered_pair(sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_29379,c_14905]) ).
tcf(c_117053,plain,
( element(ordered_pair(sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,apply(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_29763,c_14905]) ).
tcf(c_117054,plain,
( element(ordered_pair(sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1))),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31403,c_14905]) ).
tcf(c_117111,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_31594,c_87]) ).
tcf(c_117112,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31594,c_12688]) ).
tcf(c_117120,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK6(sK1,relation_dom(sK2)) = apply(sK1,empty_set) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_12764]) ).
tcf(c_117121,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_9713]) ).
tcf(c_117123,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK6(sK1,relation_dom(sK2)) = apply(sK1,empty_set) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_12807]) ).
tcf(c_117124,plain,
( in(ordered_pair(empty_set,sK6(sK1,relation_dom(sK2))),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31594,c_4623]) ).
tcf(c_117125,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_4763]) ).
tcf(c_117126,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_12637]) ).
tcf(c_117127,plain,
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK5(sK1,relation_dom(sK2)) = empty_set )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_31594,c_5251]) ).
tcf(c_117172,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_117111,c_4030]) ).
tcf(c_117173,plain,
( in(ordered_pair(sK6(sK1,relation_dom(sK2)),empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_117172,c_987,c_3611]) ).
tcf(c_117200,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38794]) ).
tcf(c_117201,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38794]) ).
tcf(c_117202,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38794]) ).
tcf(c_117203,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38794]) ).
tcf(c_117204,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38794]) ).
tcf(c_117205,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38794]) ).
tcf(c_117206,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38794]) ).
tcf(c_117207,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38794]) ).
tcf(c_117208,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38794]) ).
tcf(c_117209,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38794]) ).
tcf(c_117210,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38794]) ).
tcf(c_117211,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38794]) ).
tcf(c_117212,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38794]) ).
tcf(c_117213,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38794]) ).
tcf(c_117214,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38794]) ).
tcf(c_117215,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38794]) ).
tcf(c_117216,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38794]) ).
tcf(c_117217,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38794]) ).
tcf(c_117257,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38795]) ).
tcf(c_117258,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38795]) ).
tcf(c_117259,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38795]) ).
tcf(c_117260,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38795]) ).
tcf(c_117261,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38795]) ).
tcf(c_117262,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38795]) ).
tcf(c_117263,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38795]) ).
tcf(c_117264,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38795]) ).
tcf(c_117265,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38795]) ).
tcf(c_117266,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38795]) ).
tcf(c_117267,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38795]) ).
tcf(c_117268,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38795]) ).
tcf(c_117269,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38795]) ).
tcf(c_117270,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38795]) ).
tcf(c_117271,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38795]) ).
tcf(c_117272,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38795]) ).
tcf(c_117273,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38795]) ).
tcf(c_117274,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_rng(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38795]) ).
tcf(c_117344,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38796]) ).
tcf(c_117345,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38796]) ).
tcf(c_117346,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38796]) ).
tcf(c_117347,plain,
relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38796]) ).
tcf(c_117348,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38796]) ).
tcf(c_117349,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38796]) ).
tcf(c_117350,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38796]) ).
tcf(c_117351,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38796]) ).
tcf(c_117352,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38796]) ).
tcf(c_117353,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38796]) ).
tcf(c_117354,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38796]) ).
tcf(c_117355,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38796]) ).
tcf(c_117356,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38796]) ).
tcf(c_117357,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38796]) ).
tcf(c_117358,plain,
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38796]) ).
tcf(c_117359,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38796]) ).
tcf(c_117360,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38796]) ).
tcf(c_117361,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(relation_inverse(relation_inverse(relation_inverse(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38796]) ).
tcf(c_126309,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(relation_dom(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73,c_38906]) ).
tcf(c_126310,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(relation_rng(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_101,c_38906]) ).
tcf(c_126311,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(relation_inverse(X0)))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_121,c_38906]) ).
tcf(c_126312,plain,
relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(empty_set))))) = empty_set,
inference(superposition,[status(thm)],[c_136,c_38906]) ).
tcf(c_126313,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(X0))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11848,c_38906]) ).
tcf(c_126314,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(powerset(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_36603,c_38906]) ).
tcf(c_126315,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73332,c_38906]) ).
tcf(c_126316,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(X0)))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73336,c_38906]) ).
tcf(c_126317,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73358,c_38906]) ).
tcf(c_126318,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73360,c_38906]) ).
tcf(c_126319,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73362,c_38906]) ).
tcf(c_126320,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_rng(sK12)))))))) = empty_set )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_73361,c_38906]) ).
tcf(c_126321,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_73364,c_38906]) ).
tcf(c_126322,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK12)))))))) = empty_set )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_73363,c_38906]) ).
tcf(c_126323,plain,
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(relation_dom(sK9)))))))) = empty_set )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_73365,c_38906]) ).
tcf(c_126324,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(powerset(X0)))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_73367,c_38906]) ).
tcf(c_126325,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(sK19(sK19(powerset(X0))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89824,c_38906]) ).
tcf(c_126326,plain,
! [X0: $i] :
( ( relation_rng(relation_dom(relation_dom(relation_dom(relation_dom(sK20(powerset(sK20(sK19(sK19(powerset(X0))))))))))) = empty_set )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_89823,c_38906]) ).
fof(f91,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f92,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ( X1 = function_inverse(X0)
<~> ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(definition_folding,[],[f53,f91]) ).
fof(f93,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f91]) ).
fof(f94,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2,X3] :
( ( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| ( apply(X3,X1) = X2
& in(X1,relation_rng(X0)) ) )
& ( ( apply(X0,X2) = X1
& in(X2,relation_dom(X0))
& ( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0)) ) )
| sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f94]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| apply(X3,X1) = X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f125,plain,
! [X2,X3,X0,X1] :
( apply(X0,X2) = X1
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f95]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( in(X2,relation_dom(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f95]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f95]) ).
fof(f214,plain,
! [X3,X0,X1] :
( ~ in(X1,relation_rng(X0))
| sP0(X0,X1,apply(X3,X1),X3) ),
inference(equality_resolution,[],[f127]) ).
fof(f215,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| in(apply(X0,X2),relation_rng(X0)) ),
inference(equality_resolution,[],[f124]) ).
fof(f216,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| apply(X3,apply(X0,X2)) = X2 ),
inference(equality_resolution,[],[f123]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X1,X0,apply(X2,X0),X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X2,relation_dom(X0))
| sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP0(X0,X2,X1,X3)
| ( apply(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,X1),relation_rng(X0))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,apply(X0,X1)) = X1 )
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_2036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK3,relation_rng(sK1))
| in(X2,relation_dom(X0))
| ( X3 != sK2 )
| ( X2 != sK4 )
| ( X1 != sK3 )
| ( X0 != sK1 )
| ( relation_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_1864]) ).
tcf(c_2037,plain,
( in(sK3,relation_rng(sK1))
| in(sK4,relation_dom(sK1))
| ( relation_inverse(sK1) != sK2 )
| ( relation_rng(sK1) != relation_dom(sK2) ) ),
inference(unflattening,[status(thm)],[c_2036]) ).
tcf(c_3897,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_rng(sK1))),sK20(relation_rng(sK1)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_rng(sK1)) = empty_set )
| ~ in(apply(sK2,sK20(relation_rng(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_3515,c_49]) ).
tcf(c_3898,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_rng(sK1))),sK20(relation_rng(sK1)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_rng(sK1)) = empty_set )
| ~ in(apply(sK2,sK20(relation_rng(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_3514,c_49]) ).
tcf(c_3899,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_rng(sK1))),sK20(relation_rng(sK1)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK1) = empty_set )
| ~ in(apply(sK2,sK20(relation_rng(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_3516,c_49]) ).
tcf(c_3900,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_rng(sK1))),sK20(relation_rng(sK1)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = empty_set )
| ~ in(apply(sK2,sK20(relation_rng(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_3546,c_49]) ).
tcf(c_3901,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_rng(sK1))),sK20(relation_rng(sK1)),sK1)
| ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_rng(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_3547,c_49]) ).
tcf(c_4179,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_4169,c_49]) ).
tcf(c_4821,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(sK1,X0),X0,relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_4726,c_49]) ).
tcf(c_4838,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,sK15(sK1,X0),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_4763,c_49]) ).
tcf(c_4861,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK1,X0),X0,relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_4791,c_49]) ).
tcf(c_4954,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_1706,c_52]) ).
tcf(c_4955,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_4169,c_52]) ).
tcf(c_4956,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),X0,sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_4726,c_52]) ).
tcf(c_4957,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),X0),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(superposition,[status(thm)],[c_4763,c_52]) ).
tcf(c_4958,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),X0,apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_4791,c_52]) ).
tcf(c_4959,plain,
! [X0: $i] :
( in(apply(sK1,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(X0,relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_4954,c_4013]) ).
tcf(c_4963,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(X0,relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(light_normalisation,[status(thm)],[c_4957,c_3821,c_4030]) ).
tcf(c_4968,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),X0,apply(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_4958,c_3821,c_4030]) ).
tcf(c_4973,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),X0,sK7(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_4956,c_3821,c_4030]) ).
tcf(c_4978,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_4955,c_4013]) ).
tcf(c_4997,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,X0)) = X0 )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_1706,c_53]) ).
tcf(c_4998,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_inverse(relation_dom(sK2))) = relation_dom(sK2) )
| ( apply(X0,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_4169,c_53]) ).
tcf(c_4999,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),X0,sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_4726,c_53]) ).
tcf(c_5000,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(superposition,[status(thm)],[c_4763,c_53]) ).
tcf(c_5001,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),X0,apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_4791,c_53]) ).
tcf(c_5005,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(light_normalisation,[status(thm)],[c_5000,c_4030]) ).
tcf(c_5010,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),X0,apply(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_5001,c_4030]) ).
tcf(c_5015,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),X0,sK7(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_4999,c_4030]) ).
tcf(c_6834,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6824,c_49]) ).
tcf(c_6835,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ( apply(X0,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_6824,c_53]) ).
tcf(c_6836,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_6824,c_52]) ).
tcf(c_6857,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_inverse(relation_dom(sK2))) = relation_rng(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_6836,c_4013]) ).
tcf(c_7567,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_7557,c_49]) ).
tcf(c_7568,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ( apply(X0,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_7557,c_53]) ).
tcf(c_7569,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_7557,c_52]) ).
tcf(c_7590,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_inverse(relation_dom(sK2))) = relation_dom(relation_dom(sK2)) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_7569,c_4013]) ).
tcf(c_7708,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,sK1),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_7472,c_49]) ).
tcf(c_7709,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7472,c_53]) ).
tcf(c_7710,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7472,c_52]) ).
tcf(c_7727,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_7710,c_3821,c_4030]) ).
tcf(c_7733,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_7709,c_4030]) ).
tcf(c_8701,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8695,c_49]) ).
tcf(c_8702,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_8695,c_53]) ).
tcf(c_8703,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_8695,c_52]) ).
tcf(c_8720,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_8703,c_4013]) ).
tcf(c_10487,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(relation_inverse(sK1),X0),X0,sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_10244,c_49]) ).
tcf(c_10488,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_10244,c_53]) ).
tcf(c_10489,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_10244,c_52]) ).
tcf(c_10514,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_10489,c_4013]) ).
tcf(c_11413,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(sK1,X0),empty_set,sK2)
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_11399,c_49]) ).
tcf(c_11414,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ( apply(X1,apply(sK2,sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_11399,c_53]) ).
tcf(c_11415,plain,
! [X0: $i,X1: $i] :
( in(apply(sK2,sK7(sK1,X0)),relation_rng(sK2))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,X0) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_11399,c_52]) ).
tcf(c_13360,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,empty_set,empty_set)
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_13357,c_49]) ).
tcf(c_13361,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(empty_set,X0)) = X0 )
| ~ in(X0,relation_dom(empty_set))
| ~ sP0(empty_set,empty_set,X0,X1) ),
inference(superposition,[status(thm)],[c_13357,c_53]) ).
tcf(c_13362,plain,
! [X0: $i,X1: $i] :
( in(apply(empty_set,X0),relation_rng(empty_set))
| ~ in(X0,relation_dom(empty_set))
| ~ sP0(empty_set,empty_set,X0,X1) ),
inference(superposition,[status(thm)],[c_13357,c_52]) ).
tcf(c_13367,plain,
! [X0: $i,X1: $i] :
( in(empty_set,empty_set)
| ~ in(X0,empty_set)
| ~ sP0(empty_set,empty_set,X0,X1) ),
inference(light_normalisation,[status(thm)],[c_13362,c_3404,c_3424,c_13357]) ).
tcf(c_13368,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,empty_set) = X0 )
| ~ in(X0,empty_set)
| ~ sP0(empty_set,empty_set,X0,X1) ),
inference(light_normalisation,[status(thm)],[c_13361,c_3404,c_13357]) ).
tcf(c_13466,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(relation_inverse(sK1),X0),X0,sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_12807,c_49]) ).
tcf(c_13467,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_12807,c_53]) ).
tcf(c_13468,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_12807,c_52]) ).
tcf(c_13492,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_13468,c_4013]) ).
tcf(c_13928,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,relation_dom(sK2)),sK5(sK1,relation_dom(sK2)),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_5251,c_49]) ).
tcf(c_13929,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2)))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_5251,c_53]) ).
tcf(c_13930,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_5251,c_52]) ).
tcf(c_13963,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_13930,c_3821,c_4030]) ).
tcf(c_13969,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2)))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)),sK6(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_13929,c_4030]) ).
tcf(c_14736,plain,
! [X0: $i] :
( sP0(X0,sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK20(relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_14730,c_49]) ).
tcf(c_14737,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_14730,c_53]) ).
tcf(c_14738,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_14730,c_52]) ).
tcf(c_14761,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_14738,c_3821,c_4030]) ).
tcf(c_14766,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_14737,c_4030]) ).
tcf(c_14856,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK15(sK1,X0),X0,sK1)
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_13464,c_49]) ).
tcf(c_14857,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK15(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_13464,c_53]) ).
tcf(c_14858,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK15(sK1,X0)),relation_rng(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK15(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_13464,c_52]) ).
tcf(c_14880,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK15(sK1,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK15(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_14858,c_4013]) ).
tcf(c_14961,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1)),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6420,c_49]) ).
tcf(c_14962,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_6420,c_53]) ).
tcf(c_14963,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_6420,c_52]) ).
tcf(c_14991,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_14963,c_3821,c_4030]) ).
tcf(c_14997,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK13(sK1,relation_dom(sK1))))) = apply(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),apply(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_14962,c_4030]) ).
tcf(c_15824,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1)),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_6421,c_49]) ).
tcf(c_15825,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_6421,c_53]) ).
tcf(c_15826,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_6421,c_52]) ).
tcf(c_15859,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_15826,c_3821,c_4030]) ).
tcf(c_15865,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(sK1,relation_dom(sK1)),sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_15825,c_4030]) ).
tcf(c_17964,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,sK1),sK15(sK1,sK21(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_7060,c_49]) ).
tcf(c_17965,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7060,c_53]) ).
tcf(c_17966,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7060,c_52]) ).
tcf(c_17998,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_17966,c_3821,c_4030]) ).
tcf(c_18004,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_17965,c_4030]) ).
tcf(c_18300,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,sK1),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK21(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_7241,c_49]) ).
tcf(c_18301,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7241,c_53]) ).
tcf(c_18302,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK21(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_7241,c_52]) ).
tcf(c_18336,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_18302,c_3821,c_4030]) ).
tcf(c_18342,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(sK21(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK21(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_18301,c_4030]) ).
tcf(c_20399,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,empty_set),sK5(sK1,empty_set),relation_inverse(sK1))
| ( relation_dom(sK1) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8129,c_49]) ).
tcf(c_20400,plain,
! [X0: $i] :
( ( relation_dom(sK1) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8129,c_53]) ).
tcf(c_20401,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8129,c_52]) ).
tcf(c_20428,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK1) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_20401,c_3821,c_4030]) ).
tcf(c_20433,plain,
! [X0: $i] :
( ( relation_dom(sK1) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_20400,c_4030]) ).
tcf(c_22094,plain,
! [X0: $i] :
( sP0(X0,sK13(sK1,empty_set),sK14(sK1,empty_set),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8130,c_49]) ).
tcf(c_22095,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) )
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK13(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8130,c_53]) ).
tcf(c_22096,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK13(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8130,c_52]) ).
tcf(c_22123,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK13(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_22096,c_3821,c_4030]) ).
tcf(c_22128,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK13(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_22095,c_4030]) ).
tcf(c_22289,plain,
! [X0: $i] :
( ( apply(empty_set,apply(X0,empty_set)) = empty_set )
| ~ in(empty_set,relation_dom(X0))
| ~ in(apply(X0,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13360,c_53]) ).
tcf(c_23296,plain,
! [X0: $i] :
( sP0(X0,sK24(sK1,empty_set),sK23(sK1,empty_set),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8171,c_49]) ).
tcf(c_23297,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8171,c_53]) ).
tcf(c_23298,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( sK1 = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8171,c_52]) ).
tcf(c_23325,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_23298,c_3821,c_4030]) ).
tcf(c_23330,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_23297,c_4030]) ).
tcf(c_24251,plain,
! [X0: $i] :
( sP0(X0,sK24(empty_set,sK1),sK23(empty_set,sK1),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8174,c_49]) ).
tcf(c_24252,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_8174,c_53]) ).
tcf(c_24253,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ( sK1 = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_8174,c_52]) ).
tcf(c_24280,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_24253,c_3821,c_4030]) ).
tcf(c_24285,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_24252,c_4030]) ).
tcf(c_25200,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,empty_set),sK22(sK1,empty_set),relation_inverse(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8177,c_49]) ).
tcf(c_25201,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8177,c_53]) ).
tcf(c_25202,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_8177,c_52]) ).
tcf(c_25229,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ( relation_inverse(sK1) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_25202,c_3821,c_4030]) ).
tcf(c_25234,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_25201,c_4030]) ).
tcf(c_26649,plain,
! [X0: $i] :
( sP0(X0,sK22(empty_set,sK1),sK21(empty_set,sK1),relation_inverse(sK1))
| ( sK1 = empty_set )
| ~ in(sK22(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_26641,c_49]) ).
tcf(c_26650,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_26641,c_53]) ).
tcf(c_26651,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ( sK1 = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_26641,c_52]) ).
tcf(c_26678,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ( sK1 = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_26651,c_3821,c_4030]) ).
tcf(c_26683,plain,
! [X0: $i] :
( ( sK1 = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_26650,c_4030]) ).
tcf(c_27239,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK20(relation_dom(sK2))),empty_set,sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8706,c_49]) ).
tcf(c_27240,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(X0,apply(sK1,apply(sK2,sK20(relation_dom(sK2))))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ in(apply(sK2,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,empty_set,apply(sK2,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_8706,c_53]) ).
tcf(c_28862,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8770,c_49]) ).
tcf(c_28863,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8770,c_53]) ).
tcf(c_28864,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8770,c_52]) ).
tcf(c_28892,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_28864,c_3821,c_4030]) ).
tcf(c_28898,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),apply(sK1,sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_28863,c_4030]) ).
tcf(c_29372,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8771,c_49]) ).
tcf(c_29373,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8771,c_53]) ).
tcf(c_29374,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8771,c_52]) ).
tcf(c_29407,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_29374,c_3821,c_4030]) ).
tcf(c_29413,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_29373,c_4030]) ).
tcf(c_29757,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8797,c_49]) ).
tcf(c_29758,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8797,c_53]) ).
tcf(c_29759,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8797,c_52]) ).
tcf(c_29787,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_29759,c_3821,c_4030]) ).
tcf(c_29793,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),apply(sK1,sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_29758,c_4030]) ).
tcf(c_30835,plain,
~ empty(relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_10000,c_2037,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801]) ).
tcf(c_31362,plain,
~ empty(sK1),
inference(global_subsumption_just,[status(thm)],[c_4667,c_145,c_2037,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801]) ).
tcf(c_31364,plain,
~ empty(sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_4135,c_31362]) ).
tcf(c_31365,plain,
~ empty(relation_dom(sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_4128,c_31362]) ).
tcf(c_31366,plain,
~ empty(relation_inverse(sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_3712,c_31362]) ).
tcf(c_31369,plain,
~ empty(relation_dom(sK1)),
inference(backward_subsumption_resolution,[status(thm)],[c_4154,c_31366]) ).
tcf(c_31370,plain,
~ empty(relation_rng(sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_23068,c_31369]) ).
tcf(c_31374,plain,
~ empty(relation_inverse(sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_3997,c_31370]) ).
tcf(c_31396,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_8798,c_49]) ).
tcf(c_31397,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8798,c_53]) ).
tcf(c_31398,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_8798,c_52]) ).
tcf(c_31431,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_31398,c_3821,c_4030]) ).
tcf(c_31437,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,sK1),sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_31397,c_4030]) ).
tcf(c_31585,plain,
! [X0: $i,X1: $i] :
( sP0(X1,X0,sK15(sK1,X0),relation_inverse(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_9713,c_49]) ).
tcf(c_31586,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(superposition,[status(thm)],[c_9713,c_53]) ).
tcf(c_31587,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),X0),relation_rng(relation_inverse(sK1)))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(superposition,[status(thm)],[c_9713,c_52]) ).
tcf(c_31651,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(X0,relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(light_normalisation,[status(thm)],[c_31587,c_3821,c_4030]) ).
tcf(c_31656,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),X0)) = X0 )
| ~ in(X0,relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),X0,X1) ),
inference(light_normalisation,[status(thm)],[c_31586,c_4030]) ).
tcf(c_31958,plain,
apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_4723,c_2037,c_4013,c_4017,c_4154,c_4147,c_4723,c_16946,c_19508,c_30801]) ).
tcf(c_31962,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31958,c_49]) ).
tcf(c_31963,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1))))) = sK7(sK1,sK20(relation_dom(sK1))) )
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_31958,c_53]) ).
tcf(c_31964,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_31958,c_52]) ).
tcf(c_31965,plain,
( in(ordered_pair(sK7(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_31958,c_87]) ).
tcf(c_31966,plain,
( ( sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_9713]) ).
tcf(c_31967,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_31958,c_13488]) ).
tcf(c_31968,plain,
( ( apply(sK1,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))) )
| ( apply(sK2,sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_12807]) ).
tcf(c_31969,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_31958,c_4623]) ).
tcf(c_31970,plain,
( ( sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_4763]) ).
tcf(c_31979,plain,
( ( sK20(relation_dom(sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_31966,c_31958]) ).
tcf(c_31982,plain,
( in(ordered_pair(sK7(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_31965,c_4030]) ).
tcf(c_31983,plain,
( in(ordered_pair(sK7(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31982,c_987,c_3611]) ).
tcf(c_31986,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_31967,c_31958]) ).
tcf(c_31990,plain,
! [X0: $i] :
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_31964,c_3821,c_4030,c_31958]) ).
tcf(c_31994,plain,
! [X0: $i] :
( ( apply(X0,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))) )
| ~ in(sK7(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_31963,c_4030,c_31958]) ).
tcf(c_32001,plain,
apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))),
inference(global_subsumption_just,[status(thm)],[c_4760,c_2037,c_4013,c_4017,c_4147,c_4760,c_9862,c_16946,c_19508,c_30801]) ).
tcf(c_32003,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(demodulation,[status(thm)],[c_8706,c_32001]) ).
tcf(c_32007,plain,
! [X0: $i] :
( sP0(X0,sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))),relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32001,c_49]) ).
tcf(c_32008,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_32001,c_53]) ).
tcf(c_32009,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_32001,c_52]) ).
tcf(c_32010,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_32001,c_87]) ).
tcf(c_32011,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32001,c_13488]) ).
tcf(c_32012,plain,
( ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_32001,c_12807]) ).
tcf(c_32013,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32001,c_4623]) ).
tcf(c_32020,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_32010,c_4030]) ).
tcf(c_32021,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32020,c_987,c_3611]) ).
tcf(c_32024,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_32011,c_32001]) ).
tcf(c_32028,plain,
! [X0: $i] :
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_32009,c_3821,c_4030,c_32001]) ).
tcf(c_32032,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_32008,c_4030,c_32001]) ).
tcf(c_32039,plain,
apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_4788,c_2037,c_4013,c_4017,c_4154,c_4147,c_4788,c_16946,c_19508,c_30801]) ).
tcf(c_32043,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1)),relation_inverse(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32039,c_49]) ).
tcf(c_32044,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1))))) = apply(sK1,sK20(relation_dom(sK1))) )
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_32039,c_53]) ).
tcf(c_32045,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_32039,c_52]) ).
tcf(c_32046,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_32039,c_87]) ).
tcf(c_32047,plain,
( ( sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32039,c_9713]) ).
tcf(c_32048,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32039,c_13488]) ).
tcf(c_32049,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32039,c_4623]) ).
tcf(c_32050,plain,
( ( sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32039,c_4763]) ).
tcf(c_32057,plain,
( ( sK20(relation_dom(sK1)) = empty_set )
| ( sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_32047,c_32039]) ).
tcf(c_32060,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_32046,c_4030]) ).
tcf(c_32061,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32060,c_987,c_3611]) ).
tcf(c_32064,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_32048,c_32039]) ).
tcf(c_32068,plain,
! [X0: $i] :
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_32045,c_3821,c_4030,c_32039]) ).
tcf(c_32072,plain,
! [X0: $i] :
( ( apply(X0,sK20(relation_dom(sK1))) = apply(sK1,sK20(relation_dom(sK1))) )
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_32044,c_4030,c_32039]) ).
tcf(c_32079,plain,
apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_9804,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_9804,c_16946,c_19508,c_30801]) ).
tcf(c_32081,plain,
( ( relation_dom(sK1) = empty_set )
| ( sK15(sK1,sK6(sK1,empty_set)) = sK5(sK1,empty_set) ) ),
inference(demodulation,[status(thm)],[c_8129,c_32079]) ).
tcf(c_32084,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,empty_set),sK15(sK1,sK6(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32079,c_49]) ).
tcf(c_32085,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_32079,c_53]) ).
tcf(c_32086,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_32079,c_52]) ).
tcf(c_32087,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK15(sK1,sK6(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_32079,c_87]) ).
tcf(c_32088,plain,
( in(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32079,c_13488]) ).
tcf(c_32089,plain,
( ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK15(sK1,sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_32079,c_12807]) ).
tcf(c_32090,plain,
( in(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32079,c_4623]) ).
tcf(c_32097,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK15(sK1,sK6(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_32087,c_4030]) ).
tcf(c_32098,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK15(sK1,sK6(sK1,empty_set))),relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32097,c_987,c_3611]) ).
tcf(c_32101,plain,
( in(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ~ in(sK15(sK1,sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_32088,c_32079]) ).
tcf(c_32105,plain,
! [X0: $i] :
( in(sK15(sK1,sK6(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_32086,c_3821,c_4030,c_32079]) ).
tcf(c_32109,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_32085,c_4030,c_32079]) ).
tcf(c_32116,plain,
element(sK6(sK1,empty_set),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_9801,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_9801,c_16946,c_19508,c_30801]) ).
tcf(c_32118,plain,
( empty(relation_dom(sK2))
| in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32116,c_68]) ).
tcf(c_32119,plain,
in(sK6(sK1,empty_set),relation_dom(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_32118,c_31365]) ).
tcf(c_32120,plain,
~ in(relation_dom(sK2),sK6(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32119,c_70]) ).
tcf(c_32124,plain,
apply(sK1,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set),
inference(superposition,[status(thm)],[c_32119,c_12701]) ).
tcf(c_32125,plain,
apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set),
inference(superposition,[status(thm)],[c_32119,c_10144]) ).
tcf(c_32127,plain,
apply(sK1,sK15(sK1,sK6(sK1,empty_set))) = sK6(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_32124,c_32079]) ).
tcf(c_32347,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set),sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32125,c_49]) ).
tcf(c_32348,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set)))) = sK7(relation_inverse(sK1),sK6(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32125,c_53]) ).
tcf(c_32349,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32125,c_52]) ).
tcf(c_32350,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32125,c_87]) ).
tcf(c_32351,plain,
( ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32125,c_4863]) ).
tcf(c_32355,plain,
( ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK7(relation_inverse(sK1),sK6(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32125,c_4791]) ).
tcf(c_32358,plain,
( ( sK6(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_32355,c_32079,c_32125]) ).
tcf(c_32361,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32350,c_65,c_64]) ).
tcf(c_32364,plain,
! [X0: $i] :
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_32349,c_4013,c_32125]) ).
tcf(c_32365,plain,
( ( sK6(sK1,empty_set) = empty_set )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_32351,c_32125]) ).
tcf(c_32369,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = apply(X0,sK6(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_32348,c_32125]) ).
tcf(c_32379,plain,
( ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_32361,c_70]) ).
tcf(c_32380,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32361,c_69]) ).
tcf(c_32382,plain,
( in(sK6(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32361,c_106]) ).
tcf(c_32387,plain,
( ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK7(relation_inverse(sK1),sK6(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32361,c_3784]) ).
tcf(c_32388,plain,
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_32382,c_4013]) ).
tcf(c_32393,plain,
( ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_32387,c_32079]) ).
tcf(c_32683,plain,
! [X0: $i] :
( sP0(X0,sK13(sK1,empty_set),sK15(sK1,sK13(sK1,empty_set)),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_9987,c_49]) ).
tcf(c_32684,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) )
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_9987,c_53]) ).
tcf(c_32685,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_9987,c_52]) ).
tcf(c_32711,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_32685,c_3821,c_4030]) ).
tcf(c_32716,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = sK13(sK1,empty_set) )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(sK1,empty_set)),sK13(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_32684,c_4030]) ).
tcf(c_32736,plain,
element(sK5(sK1,empty_set),relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_10047,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_10047,c_16946,c_19508,c_30801]) ).
tcf(c_32738,plain,
( empty(relation_dom(sK1))
| in(sK5(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32736,c_68]) ).
tcf(c_32739,plain,
in(sK5(sK1,empty_set),relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_32738,c_31369]) ).
tcf(c_32740,plain,
~ in(relation_dom(sK1),sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32739,c_70]) ).
tcf(c_32744,plain,
sK15(relation_inverse(sK1),sK5(sK1,empty_set)) = apply(sK1,sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32739,c_12284]) ).
tcf(c_32745,plain,
apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set),
inference(superposition,[status(thm)],[c_32739,c_4619]) ).
tcf(c_32746,plain,
apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set),
inference(superposition,[status(thm)],[c_32739,c_4406]) ).
tcf(c_33207,plain,
( in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,empty_set),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_32744,c_107]) ).
tcf(c_33208,plain,
( in(ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set))),sK1)
| ~ in(sK5(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32744,c_4472]) ).
tcf(c_33209,plain,
in(ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set))),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_33208,c_32739]) ).
tcf(c_33210,plain,
( in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33207,c_3821]) ).
tcf(c_33211,plain,
in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_33210,c_3611,c_32739]) ).
tcf(c_33212,plain,
~ in(relation_inverse(sK1),ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_33211,c_70]) ).
tcf(c_33213,plain,
element(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_33211,c_69]) ).
tcf(c_33215,plain,
( in(sK5(sK1,empty_set),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_33211,c_106]) ).
tcf(c_33216,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_33211,c_78]) ).
tcf(c_33220,plain,
( in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33215,c_3821]) ).
tcf(c_33221,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33216,c_4030]) ).
tcf(c_33222,plain,
in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_33221,c_3611]) ).
tcf(c_33223,plain,
~ in(relation_dom(sK2),apply(sK1,sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_33222,c_70]) ).
tcf(c_33224,plain,
element(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)),
inference(superposition,[status(thm)],[c_33222,c_69]) ).
tcf(c_33227,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_33222,c_12701]) ).
tcf(c_33228,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_33222,c_10144]) ).
tcf(c_33229,plain,
apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_33222,c_4468]) ).
tcf(c_33230,plain,
sK15(sK1,apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_33229,c_32745]) ).
tcf(c_33234,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set),relation_inverse(sK1))
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32745,c_49]) ).
tcf(c_33235,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK5(sK1,empty_set)) )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32745,c_53]) ).
tcf(c_33236,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32745,c_52]) ).
tcf(c_33244,plain,
! [X0: $i] :
( in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33236,c_3821,c_4030,c_32745]) ).
tcf(c_33245,plain,
! [X0: $i] :
( ( apply(X0,sK5(sK1,empty_set)) = apply(sK1,sK5(sK1,empty_set)) )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33235,c_4030,c_32745]) ).
tcf(c_33246,plain,
! [X0: $i] :
( ( apply(X0,sK5(sK1,empty_set)) = apply(sK1,sK5(sK1,empty_set)) )
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33245,c_33222]) ).
tcf(c_33253,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_32746,c_49]) ).
tcf(c_33254,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set)))) = sK7(sK1,sK5(sK1,empty_set)) )
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32746,c_53]) ).
tcf(c_33255,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_32746,c_52]) ).
tcf(c_33256,plain,
( in(ordered_pair(sK7(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_32746,c_87]) ).
tcf(c_33257,plain,
( ( sK15(sK1,sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_9713]) ).
tcf(c_33258,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK5(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32746,c_13488]) ).
tcf(c_33259,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK7(sK1,sK5(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_12807]) ).
tcf(c_33260,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32746,c_4623]) ).
tcf(c_33261,plain,
( ( sK15(sK1,sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_4763]) ).
tcf(c_33270,plain,
( ( sK5(sK1,empty_set) = empty_set )
| ( sK15(sK1,sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_33257,c_32746]) ).
tcf(c_33273,plain,
( in(ordered_pair(sK7(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_33256,c_4030]) ).
tcf(c_33274,plain,
( in(ordered_pair(sK7(sK1,sK5(sK1,empty_set)),sK5(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33273,c_987,c_3611]) ).
tcf(c_33277,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK5(sK1,empty_set))) = empty_set )
| ~ in(sK5(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33258,c_32746]) ).
tcf(c_33278,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33277,c_32739]) ).
tcf(c_33281,plain,
! [X0: $i] :
( in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33255,c_3821,c_4030,c_32746]) ).
tcf(c_33282,plain,
! [X0: $i] :
( ( apply(X0,sK5(sK1,empty_set)) = sK7(sK1,sK5(sK1,empty_set)) )
| ~ in(sK7(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33254,c_4030,c_32746]) ).
tcf(c_33461,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10032,c_49]) ).
tcf(c_33462,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set)))) = apply(sK1,sK14(sK1,empty_set)) )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10032,c_53]) ).
tcf(c_33463,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10032,c_52]) ).
tcf(c_33490,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33463,c_3821,c_4030]) ).
tcf(c_33495,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK14(sK1,empty_set)))) = apply(sK1,sK14(sK1,empty_set)) )
| ~ in(apply(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),apply(sK1,sK14(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_33462,c_4030]) ).
tcf(c_33899,plain,
apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_10200,c_9862,c_10200,c_30835]) ).
tcf(c_33901,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_33899,c_49]) ).
tcf(c_33902,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_33899,c_53]) ).
tcf(c_33903,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_33899,c_52]) ).
tcf(c_33904,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_87]) ).
tcf(c_33905,plain,
( ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33899,c_4863]) ).
tcf(c_33906,plain,
( ~ in(relation_dom(sK2),sK20(relation_dom(sK2)))
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_6246]) ).
tcf(c_33907,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_6247]) ).
tcf(c_33908,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_5332]) ).
tcf(c_33909,plain,
( ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33899,c_4791]) ).
tcf(c_33916,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(light_normalisation,[status(thm)],[c_33909,c_32001,c_33899]) ).
tcf(c_33919,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33904,c_65,c_64]) ).
tcf(c_33923,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(light_normalisation,[status(thm)],[c_33905,c_33899]) ).
tcf(c_33927,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(X0,sK20(relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_33902,c_33899]) ).
tcf(c_33937,plain,
( ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_33919,c_70]) ).
tcf(c_33938,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33919,c_69]) ).
tcf(c_33940,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33919,c_106]) ).
tcf(c_33945,plain,
( ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33919,c_3784]) ).
tcf(c_33946,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33940,c_4013]) ).
tcf(c_33952,plain,
( ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_33945,c_32001]) ).
tcf(c_33959,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(relation_inverse(sK1),X0),X0,sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_10201,c_49]) ).
tcf(c_33960,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(X1,apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_10201,c_53]) ).
tcf(c_33961,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_rng(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_10201,c_52]) ).
tcf(c_33978,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,sK7(relation_inverse(sK1),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_33961,c_4013]) ).
tcf(c_34062,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK14(sK1,empty_set)),sK14(sK1,empty_set),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10033,c_49]) ).
tcf(c_34063,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set)))) = sK7(sK1,sK14(sK1,empty_set)) )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10033,c_53]) ).
tcf(c_34064,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10033,c_52]) ).
tcf(c_34095,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_34064,c_3821,c_4030]) ).
tcf(c_34100,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK14(sK1,empty_set)))) = sK7(sK1,sK14(sK1,empty_set)) )
| ~ in(sK7(sK1,sK14(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,empty_set),sK7(sK1,sK14(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_34063,c_4030]) ).
tcf(c_34139,plain,
sK15(relation_inverse(sK1),sK20(relation_dom(sK1))) = apply(sK1,sK20(relation_dom(sK1))),
inference(global_subsumption_just,[status(thm)],[c_12311,c_2037,c_4013,c_4017,c_4154,c_4147,c_12311,c_16946,c_19508,c_30801]) ).
tcf(c_34141,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_34139,c_107]) ).
tcf(c_34142,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34139,c_4472]) ).
tcf(c_34145,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_34141,c_3821]) ).
tcf(c_34146,plain,
( in(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34145,c_3611]) ).
tcf(c_34149,plain,
apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_12763,c_2037,c_4013,c_4017,c_4147,c_9862,c_12763,c_16946,c_19508,c_30801]) ).
tcf(c_34151,plain,
apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)),
inference(light_normalisation,[status(thm)],[c_34149,c_32001]) ).
tcf(c_34152,plain,
! [X0: $i] :
( sP0(X0,sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)),sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_34151,c_49]) ).
tcf(c_34153,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_34151,c_53]) ).
tcf(c_34154,plain,
! [X0: $i] :
( in(apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))),relation_rng(sK1))
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_34151,c_52]) ).
tcf(c_34155,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_87]) ).
tcf(c_34156,plain,
( ~ in(relation_dom(sK2),sK20(relation_dom(sK2)))
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_6246]) ).
tcf(c_34157,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_6247]) ).
tcf(c_34158,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_5332]) ).
tcf(c_34166,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34155,c_65,c_64]) ).
tcf(c_34170,plain,
! [X0: $i] :
( ( apply(X0,sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_34153,c_34151]) ).
tcf(c_34180,plain,
( ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_34166,c_70]) ).
tcf(c_34181,plain,
( element(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34166,c_69]) ).
tcf(c_34183,plain,
( in(sK20(relation_dom(sK2)),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34166,c_106]) ).
tcf(c_34189,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_34183,c_4013]) ).
tcf(c_34311,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_34158]) ).
tcf(c_34313,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_34311,c_34151]) ).
tcf(c_34314,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( sK20(relation_dom(sK2)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34313,c_65,c_64]) ).
tcf(c_34321,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK2),sK20(relation_dom(sK2))) ),
inference(superposition,[status(thm)],[c_34314,c_70]) ).
tcf(c_34322,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( sK20(relation_dom(sK2)) = empty_set ) ),
inference(superposition,[status(thm)],[c_34314,c_69]) ).
tcf(c_34325,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34314,c_12701]) ).
tcf(c_34342,plain,
( ( apply(sK1,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_12764]) ).
tcf(c_34359,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK7(sK1,sK5(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_12764]) ).
tcf(c_34360,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(relation_inverse(sK1),X0),X0,sK1)
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_12764,c_49]) ).
tcf(c_34361,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(X1,apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_12764,c_53]) ).
tcf(c_34362,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_rng(sK1))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_12764,c_52]) ).
tcf(c_34373,plain,
( ( sK5(sK1,empty_set) = empty_set )
| ( apply(sK1,sK5(sK1,empty_set)) = sK7(sK1,sK5(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_34359,c_32746]) ).
tcf(c_34385,plain,
( ( sK20(relation_dom(sK1)) = empty_set )
| ( apply(sK1,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_34342,c_31958]) ).
tcf(c_34407,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_dom(sK2))
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(relation_inverse(sK1),X0),X1) ),
inference(light_normalisation,[status(thm)],[c_34362,c_4013]) ).
tcf(c_34540,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_34529]) ).
tcf(c_34541,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32001,c_34529]) ).
tcf(c_34542,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32039,c_34529]) ).
tcf(c_34549,plain,
( in(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_32079,c_34529]) ).
tcf(c_34563,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_34529]) ).
tcf(c_34582,plain,
( in(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( sK15(sK1,sK6(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34549,c_32079]) ).
tcf(c_34585,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK15(sK1,sK20(relation_dom(sK2))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34541,c_32001]) ).
tcf(c_34591,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( sK5(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34563,c_32746]) ).
tcf(c_34603,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( sK20(relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34542,c_32039]) ).
tcf(c_34606,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( sK20(relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34540,c_31958]) ).
tcf(c_34719,plain,
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_34571]) ).
tcf(c_34720,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32001,c_34571]) ).
tcf(c_34721,plain,
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32039,c_34571]) ).
tcf(c_34728,plain,
( in(sK15(sK1,sK6(sK1,empty_set)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_32079,c_34571]) ).
tcf(c_34754,plain,
( in(sK15(sK1,sK6(sK1,empty_set)),relation_dom(sK1))
| ( sK15(sK1,sK6(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34728,c_32079]) ).
tcf(c_34757,plain,
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ( sK20(relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34721,c_32039]) ).
tcf(c_34760,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ( sK15(sK1,sK20(relation_dom(sK2))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34720,c_32001]) ).
tcf(c_34821,plain,
( element(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_31958,c_34565]) ).
tcf(c_34822,plain,
( element(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32001,c_34565]) ).
tcf(c_34823,plain,
( element(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32039,c_34565]) ).
tcf(c_34830,plain,
( element(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_32079,c_34565]) ).
tcf(c_34843,plain,
( element(ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32745,c_34565]) ).
tcf(c_34844,plain,
( element(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32746,c_34565]) ).
tcf(c_34846,plain,
( element(ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( sK15(sK1,sK6(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34830,c_32079]) ).
tcf(c_34849,plain,
( element(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK15(sK1,sK20(relation_dom(sK2))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34822,c_32001]) ).
tcf(c_34855,plain,
( element(ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set))),sK1)
| ( sK5(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34844,c_32746]) ).
tcf(c_34858,plain,
( element(ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( sK5(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34843,c_32745]) ).
tcf(c_34870,plain,
( element(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( sK20(relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34823,c_32039]) ).
tcf(c_34873,plain,
( element(ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1)))),sK1)
| ( sK20(relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_34821,c_31958]) ).
tcf(c_35501,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10207,c_49]) ).
tcf(c_35502,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))) = sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_10207,c_53]) ).
tcf(c_35503,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_10207,c_52]) ).
tcf(c_35535,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_35503,c_4013]) ).
tcf(c_35840,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_33908]) ).
tcf(c_35841,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34011,c_33908]) ).
tcf(c_35842,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( sK15(sK1,sK20(relation_dom(sK2))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_35841,c_32001]) ).
tcf(c_35853,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10226,c_49]) ).
tcf(c_35854,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1)))) = sK7(relation_inverse(sK1),sK22(sK1,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),sK7(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_10226,c_53]) ).
tcf(c_35855,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),sK7(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_10226,c_52]) ).
tcf(c_35875,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),sK7(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_35855,c_4013]) ).
tcf(c_36178,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_31958,c_34564]) ).
tcf(c_36179,plain,
( ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(superposition,[status(thm)],[c_32001,c_34564]) ).
tcf(c_36180,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_32039,c_34564]) ).
tcf(c_36187,plain,
( ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_32079,c_34564]) ).
tcf(c_36200,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_32745,c_34564]) ).
tcf(c_36201,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_32746,c_34564]) ).
tcf(c_36202,plain,
( ( sK15(sK1,sK6(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK6(sK1,empty_set)),sK6(sK1,empty_set))) ),
inference(light_normalisation,[status(thm)],[c_36187,c_32079]) ).
tcf(c_36205,plain,
( ( sK15(sK1,sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2)))) ),
inference(light_normalisation,[status(thm)],[c_36179,c_32001]) ).
tcf(c_36208,plain,
( ( sK5(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK5(sK1,empty_set),sK7(sK1,sK5(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_36201,c_32746]) ).
tcf(c_36211,plain,
( ( sK5(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_36200,c_32745]) ).
tcf(c_36223,plain,
( ( sK20(relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_36180,c_32039]) ).
tcf(c_36226,plain,
( ( sK20(relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK20(relation_dom(sK1)),sK7(sK1,sK20(relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_36178,c_31958]) ).
tcf(c_36469,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10228,c_49]) ).
tcf(c_36470,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1)))) = sK7(relation_inverse(sK1),sK21(sK1,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),sK7(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_10228,c_53]) ).
tcf(c_36471,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),sK7(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_10228,c_52]) ).
tcf(c_36491,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),sK7(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_36471,c_4013]) ).
tcf(c_36540,plain,
apply(relation_inverse(sK1),sK20(sK19(relation_dom(sK2)))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_36525,c_31365]) ).
tcf(c_36541,plain,
apply(sK1,sK7(relation_inverse(sK1),sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_36524,c_31365]) ).
tcf(c_36542,plain,
apply(sK1,apply(relation_inverse(sK1),sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_36523,c_31365]) ).
tcf(c_36543,plain,
apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_36521,c_31369]) ).
tcf(c_36544,plain,
apply(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_36520,c_31369]) ).
tcf(c_36545,plain,
sK15(relation_inverse(sK1),sK20(sK19(relation_dom(sK1)))) = apply(sK1,sK20(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_36519,c_31369]) ).
tcf(c_38352,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_10231,c_49]) ).
tcf(c_38353,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set)))) = sK7(relation_inverse(sK1),sK13(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),sK7(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10231,c_53]) ).
tcf(c_38354,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),sK7(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_10231,c_52]) ).
tcf(c_38371,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),sK7(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_38354,c_4013]) ).
tcf(c_38626,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(relation_inverse(sK1),X0),empty_set,sK1)
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ~ in(sK7(relation_inverse(sK1),X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_10494,c_49]) ).
tcf(c_38627,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(X1,apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(sK7(relation_inverse(sK1),X0),relation_dom(sK1))
| ~ sP0(sK1,empty_set,sK7(relation_inverse(sK1),X0),X1) ),
inference(superposition,[status(thm)],[c_10494,c_53]) ).
tcf(c_38637,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_10494,c_33899]) ).
tcf(c_38641,plain,
( ( sK6(sK1,empty_set) = empty_set )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK7(relation_inverse(sK1),sK6(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_10494,c_32125]) ).
tcf(c_38688,plain,
~ in(relation_dom(sK2),sK24(sK1,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_17834,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_17834,c_19508,c_30801]) ).
tcf(c_38826,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK13(sK1,X0),sK14(sK1,X0),relation_inverse(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_10593,c_49]) ).
tcf(c_38827,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) )
| ~ in(sK13(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,X0),sK13(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_10593,c_53]) ).
tcf(c_38828,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK14(sK1,X0),sK13(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_10593,c_52]) ).
tcf(c_38877,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK13(sK1,X0)),relation_dom(sK1))
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ~ in(sK13(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,X0),sK13(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_38828,c_3821,c_4030]) ).
tcf(c_38883,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK13(sK1,X0))) = sK13(sK1,X0) )
| ~ in(sK13(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK14(sK1,X0),sK13(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_38827,c_4030]) ).
tcf(c_39019,plain,
apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_17838,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_17838,c_19508,c_30801]) ).
tcf(c_39021,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_9713,c_39019]) ).
tcf(c_39022,plain,
( ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_4763,c_39019]) ).
tcf(c_39023,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8171,c_39019]) ).
tcf(c_39024,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39019,c_49]) ).
tcf(c_39025,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set)))) = apply(relation_inverse(sK1),sK24(sK1,empty_set)) )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),apply(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39019,c_53]) ).
tcf(c_39026,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))),relation_rng(sK1))
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),apply(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39019,c_52]) ).
tcf(c_39027,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39019,c_87]) ).
tcf(c_39028,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ( apply(sK2,apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39019,c_4863]) ).
tcf(c_39030,plain,
( element(sK24(sK1,empty_set),relation_dom(sK2))
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39019,c_6247]) ).
tcf(c_39031,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39019,c_5332]) ).
tcf(c_39044,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39027,c_65,c_64]) ).
tcf(c_39048,plain,
( ( sK24(sK1,empty_set) = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_39028,c_39019]) ).
tcf(c_39052,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = apply(X0,sK24(sK1,empty_set)) )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),apply(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39025,c_39019]) ).
tcf(c_39068,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_39044]) ).
tcf(c_39069,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_39044]) ).
tcf(c_39070,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK1 = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8171,c_39044]) ).
tcf(c_39071,plain,
( ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39044,c_70]) ).
tcf(c_39072,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39044,c_69]) ).
tcf(c_39074,plain,
( in(sK24(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39044,c_106]) ).
tcf(c_39080,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39074,c_4013]) ).
tcf(c_39295,plain,
in(sK24(sK1,empty_set),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_39031,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_8147,c_16946,c_19508,c_30801]) ).
tcf(c_39298,plain,
element(sK24(sK1,empty_set),relation_dom(sK2)),
inference(superposition,[status(thm)],[c_39295,c_69]) ).
tcf(c_39302,plain,
apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set),
inference(superposition,[status(thm)],[c_39295,c_10144]) ).
tcf(c_39303,plain,
apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39295,c_4468]) ).
tcf(c_39304,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(demodulation,[status(thm)],[c_39044,c_39303]) ).
tcf(c_39305,plain,
apply(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set),
inference(demodulation,[status(thm)],[c_39019,c_39303]) ).
tcf(c_39306,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(sK1,empty_set)) = sK23(sK1,empty_set) ) ),
inference(demodulation,[status(thm)],[c_8171,c_39303]) ).
tcf(c_39416,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39302,c_49]) ).
tcf(c_39417,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set)))) = sK7(relation_inverse(sK1),sK24(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39302,c_53]) ).
tcf(c_39418,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39302,c_52]) ).
tcf(c_39419,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39302,c_87]) ).
tcf(c_39420,plain,
( ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39302,c_4863]) ).
tcf(c_39424,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK7(relation_inverse(sK1),sK24(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39302,c_4791]) ).
tcf(c_39425,plain,
( ( sK24(sK1,empty_set) = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK7(relation_inverse(sK1),sK24(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_39302,c_10494]) ).
tcf(c_39428,plain,
( ( sK24(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_39424,c_39302,c_39303]) ).
tcf(c_39431,plain,
( ( sK24(sK1,empty_set) = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_39425,c_39303]) ).
tcf(c_39435,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39419,c_65,c_64]) ).
tcf(c_39438,plain,
! [X0: $i] :
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39418,c_4013,c_39302]) ).
tcf(c_39440,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = apply(X0,sK24(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39417,c_39302]) ).
tcf(c_39450,plain,
( ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39435,c_70]) ).
tcf(c_39451,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39435,c_69]) ).
tcf(c_39453,plain,
( in(sK24(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39435,c_106]) ).
tcf(c_39458,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK7(relation_inverse(sK1),sK24(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39435,c_3784]) ).
tcf(c_39459,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39453,c_4013]) ).
tcf(c_39464,plain,
( ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39458,c_39303]) ).
tcf(c_39467,plain,
! [X0: $i] :
( sP0(X0,sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39303,c_49]) ).
tcf(c_39468,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_39303,c_53]) ).
tcf(c_39469,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_39303,c_52]) ).
tcf(c_39470,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_39303,c_87]) ).
tcf(c_39471,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39303,c_34564]) ).
tcf(c_39472,plain,
( element(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39303,c_34565]) ).
tcf(c_39473,plain,
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39303,c_34571]) ).
tcf(c_39478,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39303,c_4623]) ).
tcf(c_39479,plain,
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ( sK15(sK1,sK24(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_39473,c_39303]) ).
tcf(c_39482,plain,
in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_39478,c_39295]) ).
tcf(c_39485,plain,
( element(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( sK15(sK1,sK24(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_39472,c_39303]) ).
tcf(c_39488,plain,
( ( sK15(sK1,sK24(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set))) ),
inference(light_normalisation,[status(thm)],[c_39471,c_39303]) ).
tcf(c_39491,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_39470,c_4030]) ).
tcf(c_39492,plain,
in(ordered_pair(sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_39491,c_987,c_3611,c_39295]) ).
tcf(c_39493,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_39469,c_3821,c_4030,c_39303]) ).
tcf(c_39494,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39493,c_39295]) ).
tcf(c_39497,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_39468,c_4030,c_39303]) ).
tcf(c_39498,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39497,c_39295]) ).
tcf(c_39503,plain,
~ in(relation_inverse(sK1),ordered_pair(sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39492,c_70]) ).
tcf(c_39504,plain,
element(ordered_pair(sK24(sK1,empty_set),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_39492,c_69]) ).
tcf(c_39506,plain,
( in(sK15(sK1,sK24(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_39492,c_106]) ).
tcf(c_39507,plain,
( in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_39492,c_78]) ).
tcf(c_39511,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39507,c_4030]) ).
tcf(c_39512,plain,
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39506,c_3821]) ).
tcf(c_39513,plain,
in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_39512,c_3611]) ).
tcf(c_39514,plain,
~ in(relation_dom(sK1),sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_70]) ).
tcf(c_39515,plain,
element(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1)),
inference(superposition,[status(thm)],[c_39513,c_69]) ).
tcf(c_39518,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set))) = apply(sK1,sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_12284]) ).
tcf(c_39519,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39513,c_4619]) ).
tcf(c_39520,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39513,c_4406]) ).
tcf(c_39523,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_39518,c_39305]) ).
tcf(c_39524,plain,
apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_19097,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19097,c_19508,c_30801]) ).
tcf(c_39526,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_9713,c_39524]) ).
tcf(c_39527,plain,
( ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_4763,c_39524]) ).
tcf(c_39528,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8174,c_39524]) ).
tcf(c_39529,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39524,c_49]) ).
tcf(c_39530,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1)))) = apply(relation_inverse(sK1),sK24(empty_set,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),apply(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_39524,c_53]) ).
tcf(c_39531,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))),relation_rng(sK1))
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),apply(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_39524,c_52]) ).
tcf(c_39532,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39524,c_87]) ).
tcf(c_39533,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ( apply(sK2,apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39524,c_4863]) ).
tcf(c_39534,plain,
( ~ in(relation_dom(sK2),sK24(empty_set,sK1))
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39524,c_6246]) ).
tcf(c_39535,plain,
( element(sK24(empty_set,sK1),relation_dom(sK2))
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39524,c_6247]) ).
tcf(c_39536,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39524,c_5332]) ).
tcf(c_39551,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39532,c_65,c_64]) ).
tcf(c_39555,plain,
( ( sK24(empty_set,sK1) = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_39533,c_39524]) ).
tcf(c_39559,plain,
! [X0: $i] :
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = apply(X0,sK24(empty_set,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),apply(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_39530,c_39524]) ).
tcf(c_39669,plain,
in(sK21(sK1,empty_set),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_8161,c_136,c_2037,c_4013,c_4017,c_4147,c_5811,c_8161,c_16946,c_19508,c_30801]) ).
tcf(c_39671,plain,
~ in(relation_dom(sK2),sK21(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39669,c_70]) ).
tcf(c_39672,plain,
element(sK21(sK1,empty_set),relation_dom(sK2)),
inference(superposition,[status(thm)],[c_39669,c_69]) ).
tcf(c_39675,plain,
apply(sK1,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set),
inference(superposition,[status(thm)],[c_39669,c_12701]) ).
tcf(c_39676,plain,
apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set),
inference(superposition,[status(thm)],[c_39669,c_10144]) ).
tcf(c_39677,plain,
apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39669,c_4468]) ).
tcf(c_39678,plain,
( ( relation_inverse(sK1) = empty_set )
| ( sK15(sK1,sK21(sK1,empty_set)) = sK22(sK1,empty_set) ) ),
inference(demodulation,[status(thm)],[c_8177,c_39677]) ).
tcf(c_39686,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_9713,c_39551]) ).
tcf(c_39687,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_4763,c_39551]) ).
tcf(c_39688,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK1 = empty_set )
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8174,c_39551]) ).
tcf(c_39689,plain,
( ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_39551,c_70]) ).
tcf(c_39690,plain,
( element(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39551,c_69]) ).
tcf(c_39692,plain,
( in(sK24(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39551,c_106]) ).
tcf(c_39698,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39692,c_4013]) ).
tcf(c_39713,plain,
apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_39675,c_39677]) ).
tcf(c_39714,plain,
! [X0: $i] :
( sP0(X0,sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39713,c_49]) ).
tcf(c_39715,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)) )
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39713,c_53]) ).
tcf(c_39716,plain,
! [X0: $i] :
( in(apply(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_rng(sK1))
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39713,c_52]) ).
tcf(c_39717,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39713,c_87]) ).
tcf(c_39724,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39717,c_65,c_64]) ).
tcf(c_39727,plain,
! [X0: $i] :
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39716,c_4013,c_39713]) ).
tcf(c_39728,plain,
! [X0: $i] :
( ( apply(X0,sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) )
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39715,c_39713]) ).
tcf(c_39738,plain,
( ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39724,c_70]) ).
tcf(c_39739,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39724,c_69]) ).
tcf(c_39741,plain,
( in(sK21(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39724,c_106]) ).
tcf(c_39747,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39741,c_4013]) ).
tcf(c_39753,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set),sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39676,c_49]) ).
tcf(c_39754,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set)))) = sK7(relation_inverse(sK1),sK21(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39676,c_53]) ).
tcf(c_39755,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_39676,c_52]) ).
tcf(c_39756,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39676,c_87]) ).
tcf(c_39757,plain,
( ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39676,c_4863]) ).
tcf(c_39761,plain,
( ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK7(relation_inverse(sK1),sK21(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39676,c_4791]) ).
tcf(c_39762,plain,
( ( sK21(sK1,empty_set) = empty_set )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK7(relation_inverse(sK1),sK21(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_39676,c_10494]) ).
tcf(c_39765,plain,
( ( sK21(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_39761,c_39676,c_39677]) ).
tcf(c_39768,plain,
( ( sK21(sK1,empty_set) = empty_set )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_39762,c_39677]) ).
tcf(c_39772,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39756,c_65,c_64]) ).
tcf(c_39775,plain,
! [X0: $i] :
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39755,c_4013,c_39676]) ).
tcf(c_39777,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = apply(X0,sK21(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_39754,c_39676]) ).
tcf(c_39787,plain,
( ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39772,c_70]) ).
tcf(c_39788,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39772,c_69]) ).
tcf(c_39790,plain,
( in(sK21(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39772,c_106]) ).
tcf(c_39795,plain,
( ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK7(relation_inverse(sK1),sK21(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39772,c_3784]) ).
tcf(c_39796,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39790,c_4013]) ).
tcf(c_39801,plain,
( ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39795,c_39677]) ).
tcf(c_39821,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39677,c_49]) ).
tcf(c_39822,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_39677,c_53]) ).
tcf(c_39823,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_39677,c_52]) ).
tcf(c_39824,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_39677,c_87]) ).
tcf(c_39825,plain,
( ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_39677,c_34564]) ).
tcf(c_39826,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39677,c_34565]) ).
tcf(c_39827,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_39677,c_34571]) ).
tcf(c_39832,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39677,c_4623]) ).
tcf(c_39833,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ( sK15(sK1,sK21(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_39827,c_39677]) ).
tcf(c_39836,plain,
in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_39832,c_39669]) ).
tcf(c_39839,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( sK15(sK1,sK21(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_39826,c_39677]) ).
tcf(c_39842,plain,
( ( sK15(sK1,sK21(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set))) ),
inference(light_normalisation,[status(thm)],[c_39825,c_39677]) ).
tcf(c_39845,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_39824,c_4030]) ).
tcf(c_39846,plain,
in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_39845,c_987,c_3611,c_39669]) ).
tcf(c_39847,plain,
! [X0: $i] :
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_39823,c_3821,c_4030,c_39677]) ).
tcf(c_39848,plain,
! [X0: $i] :
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39847,c_39669]) ).
tcf(c_39851,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_39822,c_4030,c_39677]) ).
tcf(c_39852,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39851,c_39669]) ).
tcf(c_39887,plain,
~ in(relation_inverse(sK1),ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39846,c_70]) ).
tcf(c_39888,plain,
element(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_39846,c_69]) ).
tcf(c_39890,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_39846,c_106]) ).
tcf(c_39891,plain,
( in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_39846,c_78]) ).
tcf(c_39895,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39891,c_4030]) ).
tcf(c_39896,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_39890,c_3821]) ).
tcf(c_39897,plain,
in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_39896,c_3611]) ).
tcf(c_39936,plain,
~ in(relation_dom(sK1),sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_70]) ).
tcf(c_39937,plain,
element(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)),
inference(superposition,[status(thm)],[c_39897,c_69]) ).
tcf(c_39940,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set))) = apply(sK1,sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_12284]) ).
tcf(c_39941,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39897,c_4619]) ).
tcf(c_39942,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)),
inference(superposition,[status(thm)],[c_39897,c_4406]) ).
tcf(c_39945,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_39940,c_39713]) ).
tcf(c_40091,plain,
element(sK22(empty_set,sK1),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_40075,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801,c_40075]) ).
tcf(c_40093,plain,
( empty(relation_dom(sK2))
| in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40091,c_68]) ).
tcf(c_40094,plain,
in(sK22(empty_set,sK1),relation_dom(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_40093,c_31365]) ).
tcf(c_40095,plain,
~ in(relation_dom(sK2),sK22(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40094,c_70]) ).
tcf(c_40099,plain,
apply(sK1,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1),
inference(superposition,[status(thm)],[c_40094,c_12701]) ).
tcf(c_40100,plain,
apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1),
inference(superposition,[status(thm)],[c_40094,c_10144]) ).
tcf(c_40101,plain,
apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40094,c_4468]) ).
tcf(c_40102,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK22(empty_set,sK1)) = sK21(empty_set,sK1) ) ),
inference(demodulation,[status(thm)],[c_26641,c_40101]) ).
tcf(c_40105,plain,
apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_40099,c_40101]) ).
tcf(c_40106,plain,
! [X0: $i] :
( sP0(X0,sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40105,c_49]) ).
tcf(c_40107,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)) )
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40105,c_53]) ).
tcf(c_40108,plain,
! [X0: $i] :
( in(apply(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_rng(sK1))
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40105,c_52]) ).
tcf(c_40109,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40105,c_87]) ).
tcf(c_40116,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40109,c_65,c_64]) ).
tcf(c_40119,plain,
! [X0: $i] :
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40108,c_4013,c_40105]) ).
tcf(c_40120,plain,
! [X0: $i] :
( ( apply(X0,sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) )
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40107,c_40105]) ).
tcf(c_40130,plain,
( ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_40116,c_70]) ).
tcf(c_40131,plain,
( element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40116,c_69]) ).
tcf(c_40133,plain,
( in(sK22(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40116,c_106]) ).
tcf(c_40139,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40133,c_4013]) ).
tcf(c_40308,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1),sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40100,c_49]) ).
tcf(c_40309,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1)))) = sK7(relation_inverse(sK1),sK22(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40100,c_53]) ).
tcf(c_40310,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40100,c_52]) ).
tcf(c_40311,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40100,c_87]) ).
tcf(c_40312,plain,
( ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40100,c_4863]) ).
tcf(c_40316,plain,
( ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK7(relation_inverse(sK1),sK22(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40100,c_4791]) ).
tcf(c_40317,plain,
( ( sK22(empty_set,sK1) = empty_set )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK7(relation_inverse(sK1),sK22(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_40100,c_10494]) ).
tcf(c_40320,plain,
( ( sK22(empty_set,sK1) = empty_set )
| ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_40316,c_40100,c_40101]) ).
tcf(c_40323,plain,
( ( sK22(empty_set,sK1) = empty_set )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_40317,c_40101]) ).
tcf(c_40327,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40311,c_65,c_64]) ).
tcf(c_40330,plain,
! [X0: $i] :
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40310,c_4013,c_40100]) ).
tcf(c_40332,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = apply(X0,sK22(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40309,c_40100]) ).
tcf(c_40342,plain,
( ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_40327,c_70]) ).
tcf(c_40343,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40327,c_69]) ).
tcf(c_40345,plain,
( in(sK22(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40327,c_106]) ).
tcf(c_40350,plain,
( ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK7(relation_inverse(sK1),sK22(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40327,c_3784]) ).
tcf(c_40351,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40345,c_4013]) ).
tcf(c_40356,plain,
( ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40350,c_40101]) ).
tcf(c_40359,plain,
! [X0: $i] :
( sP0(X0,sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40101,c_49]) ).
tcf(c_40360,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_40101,c_53]) ).
tcf(c_40361,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_40101,c_52]) ).
tcf(c_40362,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40101,c_87]) ).
tcf(c_40363,plain,
( ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_40101,c_34564]) ).
tcf(c_40364,plain,
( element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40101,c_34565]) ).
tcf(c_40365,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40101,c_34571]) ).
tcf(c_40370,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40101,c_4623]) ).
tcf(c_40371,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ( sK15(sK1,sK22(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40365,c_40101]) ).
tcf(c_40374,plain,
in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_40370,c_40094]) ).
tcf(c_40377,plain,
( element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( sK15(sK1,sK22(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40364,c_40101]) ).
tcf(c_40380,plain,
( ( sK15(sK1,sK22(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1))) ),
inference(light_normalisation,[status(thm)],[c_40363,c_40101]) ).
tcf(c_40383,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_40362,c_4030]) ).
tcf(c_40384,plain,
in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40383,c_987,c_3611,c_40094]) ).
tcf(c_40385,plain,
! [X0: $i] :
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_40361,c_3821,c_4030,c_40101]) ).
tcf(c_40386,plain,
! [X0: $i] :
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40385,c_40094]) ).
tcf(c_40389,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_40360,c_4030,c_40101]) ).
tcf(c_40390,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40389,c_40094]) ).
tcf(c_40396,plain,
~ in(relation_inverse(sK1),ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40384,c_70]) ).
tcf(c_40397,plain,
element(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_40384,c_69]) ).
tcf(c_40399,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40384,c_106]) ).
tcf(c_40400,plain,
( in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40384,c_78]) ).
tcf(c_40404,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40400,c_4030]) ).
tcf(c_40405,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40399,c_3821]) ).
tcf(c_40406,plain,
in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40405,c_3611]) ).
tcf(c_40607,plain,
~ in(relation_dom(sK1),sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_70]) ).
tcf(c_40608,plain,
element(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)),
inference(superposition,[status(thm)],[c_40406,c_69]) ).
tcf(c_40611,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1))) = apply(sK1,sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_12284]) ).
tcf(c_40612,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40406,c_4619]) ).
tcf(c_40613,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40406,c_4406]) ).
tcf(c_40616,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_40611,c_40105]) ).
tcf(c_40617,plain,
in(sK24(empty_set,sK1),relation_dom(sK2)),
inference(global_subsumption_just,[status(thm)],[c_39536,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_8150,c_16946,c_19508,c_30801]) ).
tcf(c_40619,plain,
~ in(relation_dom(sK2),sK24(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40617,c_70]) ).
tcf(c_40620,plain,
element(sK24(empty_set,sK1),relation_dom(sK2)),
inference(superposition,[status(thm)],[c_40617,c_69]) ).
tcf(c_40624,plain,
apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1),
inference(superposition,[status(thm)],[c_40617,c_10144]) ).
tcf(c_40625,plain,
apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40617,c_4468]) ).
tcf(c_40626,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(demodulation,[status(thm)],[c_39551,c_40625]) ).
tcf(c_40627,plain,
apply(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1),
inference(demodulation,[status(thm)],[c_39524,c_40625]) ).
tcf(c_40628,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK24(empty_set,sK1)) = sK23(empty_set,sK1) ) ),
inference(demodulation,[status(thm)],[c_8174,c_40625]) ).
tcf(c_40653,plain,
in(sK22(sK1,empty_set),relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_9243,c_136,c_2037,c_4013,c_4017,c_4147,c_5811,c_9243,c_16946,c_19508,c_30801]) ).
tcf(c_40655,plain,
~ in(relation_dom(sK1),sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40653,c_70]) ).
tcf(c_40656,plain,
element(sK22(sK1,empty_set),relation_dom(sK1)),
inference(superposition,[status(thm)],[c_40653,c_69]) ).
tcf(c_40659,plain,
sK15(relation_inverse(sK1),sK22(sK1,empty_set)) = apply(sK1,sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40653,c_12284]) ).
tcf(c_40660,plain,
apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set),
inference(superposition,[status(thm)],[c_40653,c_4619]) ).
tcf(c_40661,plain,
apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set),
inference(superposition,[status(thm)],[c_40653,c_4406]) ).
tcf(c_40664,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40624,c_49]) ).
tcf(c_40665,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1)))) = sK7(relation_inverse(sK1),sK24(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40624,c_53]) ).
tcf(c_40666,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_40624,c_52]) ).
tcf(c_40667,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40624,c_87]) ).
tcf(c_40668,plain,
( ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40624,c_4863]) ).
tcf(c_40672,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK7(relation_inverse(sK1),sK24(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40624,c_4791]) ).
tcf(c_40673,plain,
( ( sK24(empty_set,sK1) = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK7(relation_inverse(sK1),sK24(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_40624,c_10494]) ).
tcf(c_40676,plain,
( ( sK24(empty_set,sK1) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_40672,c_40624,c_40625]) ).
tcf(c_40679,plain,
( ( sK24(empty_set,sK1) = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_40673,c_40625]) ).
tcf(c_40683,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40667,c_65,c_64]) ).
tcf(c_40686,plain,
! [X0: $i] :
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40666,c_4013,c_40624]) ).
tcf(c_40688,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = apply(X0,sK24(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_40665,c_40624]) ).
tcf(c_40698,plain,
( ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_40683,c_70]) ).
tcf(c_40699,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40683,c_69]) ).
tcf(c_40701,plain,
( in(sK24(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40683,c_106]) ).
tcf(c_40706,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK7(relation_inverse(sK1),sK24(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40683,c_3784]) ).
tcf(c_40707,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40701,c_4013]) ).
tcf(c_40712,plain,
( ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40706,c_40625]) ).
tcf(c_40715,plain,
! [X0: $i] :
( sP0(X0,sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40625,c_49]) ).
tcf(c_40716,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_40625,c_53]) ).
tcf(c_40717,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_40625,c_52]) ).
tcf(c_40718,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40625,c_87]) ).
tcf(c_40719,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_40625,c_34564]) ).
tcf(c_40720,plain,
( element(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40625,c_34565]) ).
tcf(c_40721,plain,
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40625,c_34571]) ).
tcf(c_40726,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40625,c_4623]) ).
tcf(c_40727,plain,
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ( sK15(sK1,sK24(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40721,c_40625]) ).
tcf(c_40730,plain,
in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_40726,c_40617]) ).
tcf(c_40733,plain,
( element(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( sK15(sK1,sK24(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40720,c_40625]) ).
tcf(c_40736,plain,
( ( sK15(sK1,sK24(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1))) ),
inference(light_normalisation,[status(thm)],[c_40719,c_40625]) ).
tcf(c_40739,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_40718,c_4030]) ).
tcf(c_40740,plain,
in(ordered_pair(sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40739,c_987,c_3611,c_40617]) ).
tcf(c_40741,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_40717,c_3821,c_4030,c_40625]) ).
tcf(c_40742,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40741,c_40617]) ).
tcf(c_40745,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_40716,c_4030,c_40625]) ).
tcf(c_40746,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK24(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40745,c_40617]) ).
tcf(c_40751,plain,
~ in(relation_inverse(sK1),ordered_pair(sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40740,c_70]) ).
tcf(c_40752,plain,
element(ordered_pair(sK24(empty_set,sK1),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_40740,c_69]) ).
tcf(c_40754,plain,
( in(sK15(sK1,sK24(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40740,c_106]) ).
tcf(c_40755,plain,
( in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40740,c_78]) ).
tcf(c_40759,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40755,c_4030]) ).
tcf(c_40760,plain,
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40754,c_3821]) ).
tcf(c_40761,plain,
in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40760,c_3611]) ).
tcf(c_40762,plain,
~ in(relation_dom(sK1),sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_70]) ).
tcf(c_40763,plain,
element(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1)),
inference(superposition,[status(thm)],[c_40761,c_69]) ).
tcf(c_40766,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1))) = apply(sK1,sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_12284]) ).
tcf(c_40767,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40761,c_4619]) ).
tcf(c_40768,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)),
inference(superposition,[status(thm)],[c_40761,c_4406]) ).
tcf(c_40771,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_40766,c_40627]) ).
tcf(c_40772,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,empty_set),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40659,c_107]) ).
tcf(c_40773,plain,
( in(ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set))),sK1)
| ~ in(sK22(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40659,c_4472]) ).
tcf(c_40774,plain,
in(ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set))),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_40773,c_40653]) ).
tcf(c_40775,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK22(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40772,c_3821]) ).
tcf(c_40776,plain,
in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_40775,c_3611,c_40653]) ).
tcf(c_40777,plain,
~ in(relation_inverse(sK1),ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40776,c_70]) ).
tcf(c_40778,plain,
element(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_40776,c_69]) ).
tcf(c_40780,plain,
( in(sK22(sK1,empty_set),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40776,c_106]) ).
tcf(c_40781,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_40776,c_78]) ).
tcf(c_40785,plain,
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40780,c_3821]) ).
tcf(c_40786,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40781,c_4030]) ).
tcf(c_40787,plain,
in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_40786,c_3611]) ).
tcf(c_40788,plain,
~ in(relation_dom(sK2),apply(sK1,sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40787,c_70]) ).
tcf(c_40789,plain,
element(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)),
inference(superposition,[status(thm)],[c_40787,c_69]) ).
tcf(c_40792,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40787,c_12701]) ).
tcf(c_40793,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40787,c_10144]) ).
tcf(c_40794,plain,
apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40787,c_4468]) ).
tcf(c_40795,plain,
sK15(sK1,apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_40794,c_40660]) ).
tcf(c_40840,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set),relation_inverse(sK1))
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40660,c_49]) ).
tcf(c_40841,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK22(sK1,empty_set)) )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40660,c_53]) ).
tcf(c_40842,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40660,c_52]) ).
tcf(c_40844,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_40660,c_34564]) ).
tcf(c_40845,plain,
( element(ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40660,c_34565]) ).
tcf(c_40854,plain,
( element(ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( sK22(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40845,c_40660]) ).
tcf(c_40857,plain,
( ( sK22(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_40844,c_40660]) ).
tcf(c_40860,plain,
! [X0: $i] :
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40842,c_3821,c_4030,c_40660]) ).
tcf(c_40861,plain,
! [X0: $i] :
( ( apply(X0,sK22(sK1,empty_set)) = apply(sK1,sK22(sK1,empty_set)) )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40841,c_4030,c_40660]) ).
tcf(c_40862,plain,
! [X0: $i] :
( ( apply(X0,sK22(sK1,empty_set)) = apply(sK1,sK22(sK1,empty_set)) )
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40861,c_40787]) ).
tcf(c_40869,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40661,c_49]) ).
tcf(c_40870,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set)))) = sK7(sK1,sK22(sK1,empty_set)) )
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40661,c_53]) ).
tcf(c_40871,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40661,c_52]) ).
tcf(c_40872,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40661,c_87]) ).
tcf(c_40873,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_40661,c_34564]) ).
tcf(c_40874,plain,
( element(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_34565]) ).
tcf(c_40876,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_34529]) ).
tcf(c_40877,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK7(sK1,sK22(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_12764]) ).
tcf(c_40878,plain,
( ( sK15(sK1,sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_9713]) ).
tcf(c_40879,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK22(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40661,c_13488]) ).
tcf(c_40880,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK7(sK1,sK22(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_12807]) ).
tcf(c_40881,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40661,c_4623]) ).
tcf(c_40882,plain,
( ( sK15(sK1,sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40661,c_4763]) ).
tcf(c_40891,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( sK22(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40876,c_40661]) ).
tcf(c_40894,plain,
( element(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( sK22(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40874,c_40661]) ).
tcf(c_40897,plain,
( ( sK22(sK1,empty_set) = empty_set )
| ( sK15(sK1,sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_40878,c_40661]) ).
tcf(c_40900,plain,
( ( sK22(sK1,empty_set) = empty_set )
| ( apply(sK1,sK22(sK1,empty_set)) = sK7(sK1,sK22(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_40877,c_40661]) ).
tcf(c_40903,plain,
( ( sK22(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_40873,c_40661]) ).
tcf(c_40906,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_40872,c_4030]) ).
tcf(c_40907,plain,
( in(ordered_pair(sK7(sK1,sK22(sK1,empty_set)),sK22(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40906,c_987,c_3611]) ).
tcf(c_40910,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK22(sK1,empty_set))) = empty_set )
| ~ in(sK22(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40879,c_40661]) ).
tcf(c_40911,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK22(sK1,empty_set))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40910,c_40653]) ).
tcf(c_40914,plain,
! [X0: $i] :
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40871,c_3821,c_4030,c_40661]) ).
tcf(c_40915,plain,
! [X0: $i] :
( ( apply(X0,sK22(sK1,empty_set)) = sK7(sK1,sK22(sK1,empty_set)) )
| ~ in(sK7(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK7(sK1,sK22(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40870,c_4030,c_40661]) ).
tcf(c_40921,plain,
sK15(relation_inverse(sK1),sK23(sK1,empty_set)) = apply(sK1,sK23(sK1,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_19129,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19129,c_19508,c_30801]) ).
tcf(c_40923,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK23(sK1,empty_set),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40921,c_107]) ).
tcf(c_40924,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40921,c_4472]) ).
tcf(c_40927,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40923,c_3821]) ).
tcf(c_40928,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40927,c_3611]) ).
tcf(c_40931,plain,
apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_19132,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19132,c_19508,c_30801]) ).
tcf(c_40935,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set),relation_inverse(sK1))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40931,c_49]) ).
tcf(c_40936,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set)))) = apply(sK1,sK23(sK1,empty_set)) )
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40931,c_53]) ).
tcf(c_40937,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40931,c_52]) ).
tcf(c_40938,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40931,c_87]) ).
tcf(c_40939,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_40931,c_34564]) ).
tcf(c_40940,plain,
( element(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40931,c_34565]) ).
tcf(c_40941,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40931,c_34571]) ).
tcf(c_40942,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40931,c_34529]) ).
tcf(c_40943,plain,
( ( sK15(sK1,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40931,c_9713]) ).
tcf(c_40944,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40931,c_13488]) ).
tcf(c_40945,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40931,c_4623]) ).
tcf(c_40946,plain,
( ( sK15(sK1,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) )
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40931,c_4763]) ).
tcf(c_40947,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ( sK23(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40941,c_40931]) ).
tcf(c_40956,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( sK23(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40942,c_40931]) ).
tcf(c_40959,plain,
( element(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( sK23(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40940,c_40931]) ).
tcf(c_40962,plain,
( ( sK23(sK1,empty_set) = empty_set )
| ( sK15(sK1,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_40943,c_40931]) ).
tcf(c_40965,plain,
( ( sK23(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_40939,c_40931]) ).
tcf(c_40968,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_40938,c_4030]) ).
tcf(c_40969,plain,
( in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40968,c_987,c_3611]) ).
tcf(c_40972,plain,
( in(ordered_pair(sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_40944,c_40931]) ).
tcf(c_40976,plain,
! [X0: $i] :
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40937,c_3821,c_4030,c_40931]) ).
tcf(c_40980,plain,
! [X0: $i] :
( ( apply(X0,sK23(sK1,empty_set)) = apply(sK1,sK23(sK1,empty_set)) )
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),apply(sK1,sK23(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40936,c_4030,c_40931]) ).
tcf(c_40987,plain,
apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_19133,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19133,c_19508,c_30801]) ).
tcf(c_40991,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40987,c_49]) ).
tcf(c_40992,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set)))) = sK7(sK1,sK23(sK1,empty_set)) )
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40987,c_53]) ).
tcf(c_40993,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_40987,c_52]) ).
tcf(c_40994,plain,
( in(ordered_pair(sK7(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40987,c_87]) ).
tcf(c_40995,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK1,ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_40987,c_34564]) ).
tcf(c_40996,plain,
( element(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_34565]) ).
tcf(c_40997,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_34571]) ).
tcf(c_40998,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_34529]) ).
tcf(c_40999,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_12764]) ).
tcf(c_41000,plain,
( ( sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_9713]) ).
tcf(c_41001,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40987,c_13488]) ).
tcf(c_41002,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_12807]) ).
tcf(c_41003,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40987,c_4623]) ).
tcf(c_41004,plain,
( ( sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40987,c_4763]) ).
tcf(c_41014,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( sK23(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40998,c_40987]) ).
tcf(c_41017,plain,
( element(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( sK23(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_40996,c_40987]) ).
tcf(c_41020,plain,
( ( sK23(sK1,empty_set) = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_41000,c_40987]) ).
tcf(c_41023,plain,
( ( sK23(sK1,empty_set) = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_40999,c_40987]) ).
tcf(c_41026,plain,
( ( sK23(sK1,empty_set) = empty_set )
| ~ in(sK1,ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)))) ),
inference(light_normalisation,[status(thm)],[c_40995,c_40987]) ).
tcf(c_41029,plain,
( in(ordered_pair(sK7(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_40994,c_4030]) ).
tcf(c_41030,plain,
( in(ordered_pair(sK7(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41029,c_987,c_3611]) ).
tcf(c_41033,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41001,c_40987]) ).
tcf(c_41037,plain,
! [X0: $i] :
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40993,c_3821,c_4030,c_40987]) ).
tcf(c_41041,plain,
! [X0: $i] :
( ( apply(X0,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) )
| ~ in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_40992,c_4030,c_40987]) ).
tcf(c_41048,plain,
sK15(relation_inverse(sK1),sK23(empty_set,sK1)) = apply(sK1,sK23(empty_set,sK1)),
inference(global_subsumption_just,[status(thm)],[c_19172,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19172,c_19508,c_30801]) ).
tcf(c_41050,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK23(empty_set,sK1),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41048,c_107]) ).
tcf(c_41051,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41048,c_4472]) ).
tcf(c_41054,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41050,c_3821]) ).
tcf(c_41055,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41054,c_3611]) ).
tcf(c_41114,plain,
~ in(relation_dom(sK1),sK23(sK1,empty_set)),
inference(global_subsumption_just,[status(thm)],[c_19125,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19125,c_19508,c_30801]) ).
tcf(c_41214,plain,
apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_19175,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19175,c_19508,c_30801]) ).
tcf(c_41218,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1),relation_inverse(sK1))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_41214,c_49]) ).
tcf(c_41219,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1)))) = apply(sK1,sK23(empty_set,sK1)) )
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41214,c_53]) ).
tcf(c_41220,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41214,c_52]) ).
tcf(c_41221,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41214,c_87]) ).
tcf(c_41222,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)))) ),
inference(superposition,[status(thm)],[c_41214,c_34564]) ).
tcf(c_41223,plain,
( element(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41214,c_34565]) ).
tcf(c_41224,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41214,c_34571]) ).
tcf(c_41225,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41214,c_34529]) ).
tcf(c_41226,plain,
( ( sK15(sK1,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41214,c_9713]) ).
tcf(c_41227,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41214,c_13488]) ).
tcf(c_41228,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_41214,c_4623]) ).
tcf(c_41229,plain,
( ( sK15(sK1,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) )
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41214,c_4763]) ).
tcf(c_41230,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ( sK23(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41224,c_41214]) ).
tcf(c_41239,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( sK23(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41225,c_41214]) ).
tcf(c_41242,plain,
( element(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( sK23(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41223,c_41214]) ).
tcf(c_41245,plain,
( ( sK23(empty_set,sK1) = empty_set )
| ( sK15(sK1,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_41226,c_41214]) ).
tcf(c_41248,plain,
( ( sK23(empty_set,sK1) = empty_set )
| ~ in(sK1,ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)))) ),
inference(light_normalisation,[status(thm)],[c_41222,c_41214]) ).
tcf(c_41251,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_41221,c_4030]) ).
tcf(c_41252,plain,
( in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41251,c_987,c_3611]) ).
tcf(c_41255,plain,
( in(ordered_pair(sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41227,c_41214]) ).
tcf(c_41259,plain,
! [X0: $i] :
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41220,c_3821,c_4030,c_41214]) ).
tcf(c_41263,plain,
! [X0: $i] :
( ( apply(X0,sK23(empty_set,sK1)) = apply(sK1,sK23(empty_set,sK1)) )
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),apply(sK1,sK23(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41219,c_4030,c_41214]) ).
tcf(c_41403,plain,
apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_19176,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19176,c_19508,c_30801]) ).
tcf(c_41407,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1),relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_41403,c_49]) ).
tcf(c_41408,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1)))) = sK7(sK1,sK23(empty_set,sK1)) )
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41403,c_53]) ).
tcf(c_41409,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41403,c_52]) ).
tcf(c_41410,plain,
( in(ordered_pair(sK7(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41403,c_87]) ).
tcf(c_41411,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)))) ),
inference(superposition,[status(thm)],[c_41403,c_34564]) ).
tcf(c_41412,plain,
( element(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_34565]) ).
tcf(c_41413,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_34571]) ).
tcf(c_41414,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_34529]) ).
tcf(c_41415,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_12764]) ).
tcf(c_41416,plain,
( ( sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_9713]) ).
tcf(c_41417,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41403,c_13488]) ).
tcf(c_41418,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) )
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_12807]) ).
tcf(c_41419,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_41403,c_4623]) ).
tcf(c_41420,plain,
( ( sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) )
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41403,c_4763]) ).
tcf(c_41430,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( sK23(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41414,c_41403]) ).
tcf(c_41433,plain,
( element(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( sK23(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41412,c_41403]) ).
tcf(c_41436,plain,
( ( sK23(empty_set,sK1) = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_41416,c_41403]) ).
tcf(c_41439,plain,
( ( sK23(empty_set,sK1) = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_41415,c_41403]) ).
tcf(c_41442,plain,
( ( sK23(empty_set,sK1) = empty_set )
| ~ in(sK1,ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)))) ),
inference(light_normalisation,[status(thm)],[c_41411,c_41403]) ).
tcf(c_41445,plain,
( in(ordered_pair(sK7(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_41410,c_4030]) ).
tcf(c_41446,plain,
( in(ordered_pair(sK7(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41445,c_987,c_3611]) ).
tcf(c_41449,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41417,c_41403]) ).
tcf(c_41453,plain,
! [X0: $i] :
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41409,c_3821,c_4030,c_41403]) ).
tcf(c_41457,plain,
! [X0: $i] :
( ( apply(X0,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) )
| ~ in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41408,c_4030,c_41403]) ).
tcf(c_41464,plain,
sK15(relation_inverse(sK1),sK21(empty_set,sK1)) = apply(sK1,sK21(empty_set,sK1)),
inference(global_subsumption_just,[status(thm)],[c_19288,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19288,c_19508,c_30801]) ).
tcf(c_41466,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(empty_set,sK1),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41464,c_107]) ).
tcf(c_41467,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41464,c_4472]) ).
tcf(c_41470,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41466,c_3821]) ).
tcf(c_41471,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41470,c_3611]) ).
tcf(c_41474,plain,
apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_19291,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19291,c_19508,c_30801]) ).
tcf(c_41478,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1),relation_inverse(sK1))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_41474,c_49]) ).
tcf(c_41479,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1)))) = apply(sK1,sK21(empty_set,sK1)) )
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41474,c_53]) ).
tcf(c_41480,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41474,c_52]) ).
tcf(c_41481,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41474,c_87]) ).
tcf(c_41482,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)))) ),
inference(superposition,[status(thm)],[c_41474,c_34564]) ).
tcf(c_41483,plain,
( element(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41474,c_34565]) ).
tcf(c_41484,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41474,c_34571]) ).
tcf(c_41485,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41474,c_34529]) ).
tcf(c_41486,plain,
( ( sK15(sK1,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41474,c_9713]) ).
tcf(c_41487,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41474,c_13488]) ).
tcf(c_41488,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_41474,c_4623]) ).
tcf(c_41489,plain,
( ( sK15(sK1,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) )
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41474,c_4763]) ).
tcf(c_41490,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( sK21(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41484,c_41474]) ).
tcf(c_41499,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( sK21(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41485,c_41474]) ).
tcf(c_41502,plain,
( element(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( sK21(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41483,c_41474]) ).
tcf(c_41505,plain,
( ( sK21(empty_set,sK1) = empty_set )
| ( sK15(sK1,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_41486,c_41474]) ).
tcf(c_41508,plain,
( ( sK21(empty_set,sK1) = empty_set )
| ~ in(sK1,ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)))) ),
inference(light_normalisation,[status(thm)],[c_41482,c_41474]) ).
tcf(c_41511,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_41481,c_4030]) ).
tcf(c_41512,plain,
( in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41511,c_987,c_3611]) ).
tcf(c_41515,plain,
( in(ordered_pair(sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41487,c_41474]) ).
tcf(c_41519,plain,
! [X0: $i] :
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41480,c_3821,c_4030,c_41474]) ).
tcf(c_41523,plain,
! [X0: $i] :
( ( apply(X0,sK21(empty_set,sK1)) = apply(sK1,sK21(empty_set,sK1)) )
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),apply(sK1,sK21(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41479,c_4030,c_41474]) ).
tcf(c_41530,plain,
apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_19292,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19292,c_19508,c_30801]) ).
tcf(c_41534,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1),relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_41530,c_49]) ).
tcf(c_41535,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1)))) = sK7(sK1,sK21(empty_set,sK1)) )
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41530,c_53]) ).
tcf(c_41536,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)),X0) ),
inference(superposition,[status(thm)],[c_41530,c_52]) ).
tcf(c_41537,plain,
( in(ordered_pair(sK7(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_41530,c_87]) ).
tcf(c_41538,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK1,ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)))) ),
inference(superposition,[status(thm)],[c_41530,c_34564]) ).
tcf(c_41539,plain,
( element(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_34565]) ).
tcf(c_41540,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_34571]) ).
tcf(c_41541,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_34529]) ).
tcf(c_41542,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_12764]) ).
tcf(c_41543,plain,
( ( sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_9713]) ).
tcf(c_41544,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41530,c_13488]) ).
tcf(c_41545,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) )
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_12807]) ).
tcf(c_41546,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_41530,c_4623]) ).
tcf(c_41547,plain,
( ( sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) )
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_41530,c_4763]) ).
tcf(c_41557,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( sK21(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41541,c_41530]) ).
tcf(c_41560,plain,
( element(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( sK21(empty_set,sK1) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_41539,c_41530]) ).
tcf(c_41563,plain,
( ( sK21(empty_set,sK1) = empty_set )
| ( sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_41543,c_41530]) ).
tcf(c_41566,plain,
( ( sK21(empty_set,sK1) = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_41542,c_41530]) ).
tcf(c_41569,plain,
( ( sK21(empty_set,sK1) = empty_set )
| ~ in(sK1,ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)))) ),
inference(light_normalisation,[status(thm)],[c_41538,c_41530]) ).
tcf(c_41572,plain,
( in(ordered_pair(sK7(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_41537,c_4030]) ).
tcf(c_41573,plain,
( in(ordered_pair(sK7(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41572,c_987,c_3611]) ).
tcf(c_41576,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_41544,c_41530]) ).
tcf(c_41580,plain,
! [X0: $i] :
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41536,c_3821,c_4030,c_41530]) ).
tcf(c_41584,plain,
! [X0: $i] :
( ( apply(X0,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) )
| ~ in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_41535,c_4030,c_41530]) ).
tcf(c_41591,plain,
~ in(relation_dom(sK1),sK23(empty_set,sK1)),
inference(global_subsumption_just,[status(thm)],[c_19168,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19168,c_19508,c_30801]) ).
tcf(c_41593,plain,
~ in(relation_dom(sK1),sK21(empty_set,sK1)),
inference(global_subsumption_just,[status(thm)],[c_19284,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19284,c_19508,c_30801]) ).
tcf(c_41915,plain,
! [X0: $i] :
( sP0(X0,sK5(sK1,relation_dom(sK2)),empty_set,relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_12634,c_49]) ).
tcf(c_41916,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_12634,c_53]) ).
tcf(c_41917,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_12634,c_52]) ).
tcf(c_41964,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_41917,c_3821,c_4030]) ).
tcf(c_41970,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_41916,c_4030]) ).
tcf(c_42247,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK6(sK1,X0),sK5(sK1,X0),relation_inverse(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK6(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_12637,c_49]) ).
tcf(c_42248,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) )
| ~ in(sK6(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,X0),sK6(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_12637,c_53]) ).
tcf(c_42249,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK6(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,X0),sK6(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_12637,c_52]) ).
tcf(c_42309,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,X0)),relation_dom(sK1))
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ~ in(sK6(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,X0),sK6(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_42249,c_3821,c_4030]) ).
tcf(c_42315,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK6(sK1,X0))) = sK6(sK1,X0) )
| ~ in(sK6(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,X0),sK6(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_42248,c_4030]) ).
tcf(c_42480,plain,
( ( sK15(relation_inverse(sK2),sK6(sK1,empty_set)) = apply(sK2,sK6(sK1,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_32119,c_42224]) ).
tcf(c_42482,plain,
( ( sK15(relation_inverse(sK2),sK24(empty_set,sK1)) = apply(sK2,sK24(empty_set,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_40617,c_42224]) ).
tcf(c_42483,plain,
( ( sK15(relation_inverse(sK2),sK24(sK1,empty_set)) = apply(sK2,sK24(sK1,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_39295,c_42224]) ).
tcf(c_42484,plain,
( ( sK15(relation_inverse(sK2),sK22(empty_set,sK1)) = apply(sK2,sK22(empty_set,sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_40094,c_42224]) ).
tcf(c_42485,plain,
( ( sK15(relation_inverse(sK2),sK21(sK1,empty_set)) = apply(sK2,sK21(sK1,empty_set)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_39669,c_42224]) ).
tcf(c_42516,plain,
( ( sK15(relation_inverse(sK2),apply(sK1,sK5(sK1,empty_set))) = apply(sK2,apply(sK1,sK5(sK1,empty_set))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_33222,c_42224]) ).
tcf(c_42518,plain,
( ( sK15(relation_inverse(sK2),apply(sK1,sK22(sK1,empty_set))) = apply(sK2,apply(sK1,sK22(sK1,empty_set))) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_40787,c_42224]) ).
tcf(c_42532,plain,
( ( sK15(relation_inverse(sK2),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42434,c_31365]) ).
tcf(c_42539,plain,
( ( sK15(relation_inverse(sK2),sK20(sK19(relation_dom(sK2)))) = apply(sK2,sK20(sK19(relation_dom(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42517,c_31365]) ).
tcf(c_43247,plain,
( ( apply(sK2,sK7(relation_inverse(sK2),sK20(relation_rng(sK2)))) = sK20(relation_rng(sK2)) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43190,c_31370]) ).
tcf(c_43250,plain,
( ( apply(sK2,sK7(relation_inverse(sK2),sK20(sK19(relation_rng(sK2))))) = sK20(sK19(relation_rng(sK2))) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43246,c_31370]) ).
tcf(c_49923,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),sK1)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_12770,c_49]) ).
tcf(c_49924,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))))) = apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_12770,c_53]) ).
tcf(c_49925,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_12770,c_52]) ).
tcf(c_49964,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(sK1,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_49925,c_4013]) ).
tcf(c_50395,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_33228,c_49]) ).
tcf(c_50396,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))))) = sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_33228,c_53]) ).
tcf(c_50397,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_33228,c_52]) ).
tcf(c_50398,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33228,c_87]) ).
tcf(c_50399,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33228,c_4863]) ).
tcf(c_50403,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33228,c_4791]) ).
tcf(c_50404,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK1,empty_set))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_33228,c_10494]) ).
tcf(c_50407,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_50403,c_32745,c_33228]) ).
tcf(c_50410,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50398,c_65,c_64]) ).
tcf(c_50413,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK1,empty_set))) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_50404,c_32745]) ).
tcf(c_50417,plain,
! [X0: $i] :
( in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_50397,c_4013,c_33228]) ).
tcf(c_50419,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = apply(X0,apply(sK1,sK5(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_50396,c_33228]) ).
tcf(c_50508,plain,
( ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_50410,c_70]) ).
tcf(c_50509,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_50410,c_69]) ).
tcf(c_50511,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_50410,c_106]) ).
tcf(c_50516,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_50410,c_3784]) ).
tcf(c_50517,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_50511,c_4013]) ).
tcf(c_50522,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_50516,c_32745]) ).
tcf(c_50562,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK22(sK1,sK1)),sK22(sK1,sK1),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_12789,c_49]) ).
tcf(c_50563,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1)))) = apply(relation_inverse(sK1),sK22(sK1,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),apply(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_12789,c_53]) ).
tcf(c_50564,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),apply(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_12789,c_52]) ).
tcf(c_50587,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK1,sK1),apply(relation_inverse(sK1),sK22(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_50564,c_4013]) ).
tcf(c_51029,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_33908]) ).
tcf(c_51030,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_33919]) ).
tcf(c_51031,plain,
( ( apply(relation_inverse(sK1),sK20(relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34013,c_33899]) ).
tcf(c_51038,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_32361]) ).
tcf(c_51039,plain,
( ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_34013,c_32125]) ).
tcf(c_51042,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_39435]) ).
tcf(c_51043,plain,
( ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_34013,c_39302]) ).
tcf(c_51044,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_40683]) ).
tcf(c_51045,plain,
( ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_34013,c_40624]) ).
tcf(c_51046,plain,
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_50410]) ).
tcf(c_51047,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK5(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_34013,c_33228]) ).
tcf(c_51048,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_39772]) ).
tcf(c_51049,plain,
( ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_34013,c_39676]) ).
tcf(c_51050,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_40327]) ).
tcf(c_51051,plain,
( ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_34013,c_40100]) ).
tcf(c_51122,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK21(sK1,sK1)),sK21(sK1,sK1),sK1)
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_12791,c_49]) ).
tcf(c_51123,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1)))) = apply(relation_inverse(sK1),sK21(sK1,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),apply(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_12791,c_53]) ).
tcf(c_51124,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),apply(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_12791,c_52]) ).
tcf(c_51145,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK1),apply(relation_inverse(sK1),sK21(sK1,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_51124,c_4013]) ).
tcf(c_51430,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),sK15(sK1,sK24(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39520,c_49]) ).
tcf(c_51431,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) )
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_39520,c_53]) ).
tcf(c_51432,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_39520,c_52]) ).
tcf(c_51433,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_39520,c_87]) ).
tcf(c_51434,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))))) ),
inference(superposition,[status(thm)],[c_39520,c_34564]) ).
tcf(c_51435,plain,
( element(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_34565]) ).
tcf(c_51437,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_34529]) ).
tcf(c_51438,plain,
( ( apply(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_12764]) ).
tcf(c_51439,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_9713]) ).
tcf(c_51440,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39520,c_13488]) ).
tcf(c_51441,plain,
( ( apply(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_12807]) ).
tcf(c_51442,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39520,c_4623]) ).
tcf(c_51443,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39520,c_4763]) ).
tcf(c_51450,plain,
( ( sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51441,c_39305]) ).
tcf(c_51453,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( sK15(sK1,sK24(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51437,c_39520]) ).
tcf(c_51456,plain,
( element(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( sK15(sK1,sK24(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51435,c_39520]) ).
tcf(c_51459,plain,
( ( sK15(sK1,sK24(sK1,empty_set)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_51439,c_39520]) ).
tcf(c_51462,plain,
( ( sK15(sK1,sK24(sK1,empty_set)) = empty_set )
| ( sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_51438,c_39305,c_39520]) ).
tcf(c_51465,plain,
( ( sK15(sK1,sK24(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))))) ),
inference(light_normalisation,[status(thm)],[c_51434,c_39520]) ).
tcf(c_51468,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51433,c_4030]) ).
tcf(c_51469,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),sK15(sK1,sK24(sK1,empty_set))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51468,c_987,c_3611]) ).
tcf(c_51472,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set )
| ~ in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51440,c_39520]) ).
tcf(c_51473,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51472,c_39513]) ).
tcf(c_51476,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51432,c_3821,c_4030,c_39520]) ).
tcf(c_51477,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) )
| ~ in(sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(sK1,empty_set)),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51431,c_4030,c_39520]) ).
tcf(c_51485,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),sK15(sK1,sK21(sK1,empty_set)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_39942,c_49]) ).
tcf(c_51486,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) )
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_39942,c_53]) ).
tcf(c_51487,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_39942,c_52]) ).
tcf(c_51488,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_39942,c_87]) ).
tcf(c_51489,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))))) ),
inference(superposition,[status(thm)],[c_39942,c_34564]) ).
tcf(c_51490,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_34565]) ).
tcf(c_51492,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_34529]) ).
tcf(c_51493,plain,
( ( apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_12764]) ).
tcf(c_51494,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_9713]) ).
tcf(c_51495,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39942,c_13488]) ).
tcf(c_51496,plain,
( ( apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_12807]) ).
tcf(c_51497,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39942,c_4623]) ).
tcf(c_51498,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39942,c_4763]) ).
tcf(c_51505,plain,
( ( sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51496,c_39713]) ).
tcf(c_51508,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( sK15(sK1,sK21(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51492,c_39942]) ).
tcf(c_51511,plain,
( element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( sK15(sK1,sK21(sK1,empty_set)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51490,c_39942]) ).
tcf(c_51514,plain,
( ( sK15(sK1,sK21(sK1,empty_set)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_51494,c_39942]) ).
tcf(c_51517,plain,
( ( sK15(sK1,sK21(sK1,empty_set)) = empty_set )
| ( sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_51493,c_39713,c_39942]) ).
tcf(c_51520,plain,
( ( sK15(sK1,sK21(sK1,empty_set)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))))) ),
inference(light_normalisation,[status(thm)],[c_51489,c_39942]) ).
tcf(c_51523,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51488,c_4030]) ).
tcf(c_51524,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),sK15(sK1,sK21(sK1,empty_set))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51523,c_987,c_3611]) ).
tcf(c_51527,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set )
| ~ in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51495,c_39942]) ).
tcf(c_51528,plain,
( in(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51527,c_39897]) ).
tcf(c_51531,plain,
! [X0: $i] :
( in(sK15(sK1,sK21(sK1,empty_set)),relation_dom(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51487,c_3821,c_4030,c_39942]) ).
tcf(c_51532,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK21(sK1,empty_set))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) )
| ~ in(sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,empty_set)),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51486,c_4030,c_39942]) ).
tcf(c_51577,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),sK15(sK1,sK22(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40613,c_49]) ).
tcf(c_51578,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) )
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),X0) ),
inference(superposition,[status(thm)],[c_40613,c_53]) ).
tcf(c_51579,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),X0) ),
inference(superposition,[status(thm)],[c_40613,c_52]) ).
tcf(c_51580,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40613,c_87]) ).
tcf(c_51581,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))))) ),
inference(superposition,[status(thm)],[c_40613,c_34564]) ).
tcf(c_51582,plain,
( element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_34565]) ).
tcf(c_51584,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_34529]) ).
tcf(c_51585,plain,
( ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_12764]) ).
tcf(c_51586,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_9713]) ).
tcf(c_51587,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40613,c_13488]) ).
tcf(c_51588,plain,
( ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_12807]) ).
tcf(c_51589,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40613,c_4623]) ).
tcf(c_51590,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40613,c_4763]) ).
tcf(c_51597,plain,
( ( sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51588,c_40105]) ).
tcf(c_51600,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( sK15(sK1,sK22(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51584,c_40613]) ).
tcf(c_51603,plain,
( element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( sK15(sK1,sK22(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51582,c_40613]) ).
tcf(c_51606,plain,
( ( sK15(sK1,sK22(empty_set,sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_51586,c_40613]) ).
tcf(c_51609,plain,
( ( sK15(sK1,sK22(empty_set,sK1)) = empty_set )
| ( sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_51585,c_40105,c_40613]) ).
tcf(c_51612,plain,
( ( sK15(sK1,sK22(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))))) ),
inference(light_normalisation,[status(thm)],[c_51581,c_40613]) ).
tcf(c_51615,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51580,c_4030]) ).
tcf(c_51616,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),sK15(sK1,sK22(empty_set,sK1))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51615,c_987,c_3611]) ).
tcf(c_51619,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set )
| ~ in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51587,c_40613]) ).
tcf(c_51620,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51619,c_40406]) ).
tcf(c_51623,plain,
! [X0: $i] :
( in(sK15(sK1,sK22(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_51579,c_3821,c_4030,c_40613]) ).
tcf(c_51624,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK22(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) )
| ~ in(sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(empty_set,sK1)),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_51578,c_4030,c_40613]) ).
tcf(c_51795,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),sK15(sK1,sK24(empty_set,sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40768,c_49]) ).
tcf(c_51796,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) )
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),X0) ),
inference(superposition,[status(thm)],[c_40768,c_53]) ).
tcf(c_51797,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),X0) ),
inference(superposition,[status(thm)],[c_40768,c_52]) ).
tcf(c_51798,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_40768,c_87]) ).
tcf(c_51799,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))))) ),
inference(superposition,[status(thm)],[c_40768,c_34564]) ).
tcf(c_51800,plain,
( element(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_34565]) ).
tcf(c_51802,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_34529]) ).
tcf(c_51803,plain,
( ( apply(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_12764]) ).
tcf(c_51804,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_9713]) ).
tcf(c_51805,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40768,c_13488]) ).
tcf(c_51806,plain,
( ( apply(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_12807]) ).
tcf(c_51807,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40768,c_4623]) ).
tcf(c_51808,plain,
( ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40768,c_4763]) ).
tcf(c_51815,plain,
( ( sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51806,c_40627]) ).
tcf(c_51818,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( sK15(sK1,sK24(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51802,c_40768]) ).
tcf(c_51821,plain,
( element(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( sK15(sK1,sK24(empty_set,sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_51800,c_40768]) ).
tcf(c_51824,plain,
( ( sK15(sK1,sK24(empty_set,sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_51804,c_40768]) ).
tcf(c_51827,plain,
( ( sK15(sK1,sK24(empty_set,sK1)) = empty_set )
| ( sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_51803,c_40627,c_40768]) ).
tcf(c_51830,plain,
( ( sK15(sK1,sK24(empty_set,sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))))) ),
inference(light_normalisation,[status(thm)],[c_51799,c_40768]) ).
tcf(c_51833,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51798,c_4030]) ).
tcf(c_51834,plain,
( in(ordered_pair(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),sK15(sK1,sK24(empty_set,sK1))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51833,c_987,c_3611]) ).
tcf(c_51837,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set )
| ~ in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51805,c_40768]) ).
tcf(c_51838,plain,
( in(ordered_pair(sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51837,c_40761]) ).
tcf(c_51841,plain,
! [X0: $i] :
( in(sK15(sK1,sK24(empty_set,sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_51797,c_3821,c_4030,c_40768]) ).
tcf(c_51842,plain,
! [X0: $i] :
( ( apply(X0,sK15(sK1,sK24(empty_set,sK1))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) )
| ~ in(sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK24(empty_set,sK1)),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_51796,c_4030,c_40768]) ).
tcf(c_51913,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK22(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_34013,c_40793]) ).
tcf(c_51914,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set)),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_40793,c_49]) ).
tcf(c_51915,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))))) = sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_40793,c_53]) ).
tcf(c_51916,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),relation_rng(sK1))
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),X0) ),
inference(superposition,[status(thm)],[c_40793,c_52]) ).
tcf(c_51917,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40793,c_87]) ).
tcf(c_51918,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40793,c_4863]) ).
tcf(c_51922,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40793,c_4791]) ).
tcf(c_51923,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( apply(sK2,apply(sK1,sK22(sK1,empty_set))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) ) ),
inference(superposition,[status(thm)],[c_40793,c_10494]) ).
tcf(c_51927,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_51922,c_40660,c_40793]) ).
tcf(c_51930,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51917,c_65,c_64]) ).
tcf(c_51933,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( apply(sK2,apply(sK1,sK22(sK1,empty_set))) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_51923,c_40660]) ).
tcf(c_51937,plain,
! [X0: $i] :
( in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51916,c_4013,c_40793]) ).
tcf(c_51939,plain,
! [X0: $i] :
( ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = apply(X0,apply(sK1,sK22(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),X0) ),
inference(light_normalisation,[status(thm)],[c_51915,c_40793]) ).
tcf(c_51949,plain,
( in(ordered_pair(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34013,c_51930]) ).
tcf(c_51950,plain,
( ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ~ in(sK1,ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set)))) ),
inference(superposition,[status(thm)],[c_51930,c_70]) ).
tcf(c_51951,plain,
( element(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_51930,c_69]) ).
tcf(c_51953,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_rng(sK1))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_51930,c_106]) ).
tcf(c_51958,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_51930,c_3784]) ).
tcf(c_51959,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ relation(sK1)
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51953,c_4013]) ).
tcf(c_51964,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_51958,c_40660]) ).
tcf(c_51972,plain,
( ( sK15(relation_inverse(sK2),sK6(sK1,empty_set)) = apply(sK2,sK6(sK1,empty_set)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42480]) ).
tcf(c_51974,plain,
sK15(relation_inverse(sK2),sK6(sK1,empty_set)) = apply(sK2,sK6(sK1,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_51972,c_61]) ).
tcf(c_51975,plain,
( in(ordered_pair(apply(sK2,sK6(sK1,empty_set)),sK6(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK6(sK1,empty_set),relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_51974,c_107]) ).
tcf(c_51976,plain,
( in(ordered_pair(sK6(sK1,empty_set),apply(sK2,sK6(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_51974,c_31806]) ).
tcf(c_51977,plain,
( in(ordered_pair(sK6(sK1,empty_set),apply(sK2,sK6(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51976,c_32119]) ).
tcf(c_51980,plain,
( in(ordered_pair(apply(sK2,sK6(sK1,empty_set)),sK6(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51975,c_3845]) ).
tcf(c_51981,plain,
( in(ordered_pair(apply(sK2,sK6(sK1,empty_set)),sK6(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51980,c_32119]) ).
tcf(c_51988,plain,
( ( sK15(relation_inverse(sK2),sK24(empty_set,sK1)) = apply(sK2,sK24(empty_set,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42482]) ).
tcf(c_51990,plain,
sK15(relation_inverse(sK2),sK24(empty_set,sK1)) = apply(sK2,sK24(empty_set,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_51988,c_61]) ).
tcf(c_51991,plain,
( in(ordered_pair(apply(sK2,sK24(empty_set,sK1)),sK24(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(empty_set,sK1),relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_51990,c_107]) ).
tcf(c_51992,plain,
( in(ordered_pair(sK24(empty_set,sK1),apply(sK2,sK24(empty_set,sK1))),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_51990,c_31806]) ).
tcf(c_51993,plain,
( in(ordered_pair(sK24(empty_set,sK1),apply(sK2,sK24(empty_set,sK1))),sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51992,c_40617]) ).
tcf(c_51996,plain,
( in(ordered_pair(apply(sK2,sK24(empty_set,sK1)),sK24(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_51991,c_3845]) ).
tcf(c_51997,plain,
( in(ordered_pair(apply(sK2,sK24(empty_set,sK1)),sK24(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51996,c_40617]) ).
tcf(c_52004,plain,
( ( sK15(relation_inverse(sK2),sK24(sK1,empty_set)) = apply(sK2,sK24(sK1,empty_set)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42483]) ).
tcf(c_52006,plain,
sK15(relation_inverse(sK2),sK24(sK1,empty_set)) = apply(sK2,sK24(sK1,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_52004,c_61]) ).
tcf(c_52016,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK13(sK1,empty_set)),sK13(sK1,empty_set),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_12794,c_49]) ).
tcf(c_52017,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set)))) = apply(relation_inverse(sK1),sK13(sK1,empty_set)) )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),apply(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_12794,c_53]) ).
tcf(c_52018,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),apply(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(superposition,[status(thm)],[c_12794,c_52]) ).
tcf(c_52035,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_dom(sK1))
| ~ sP0(sK1,sK13(sK1,empty_set),apply(relation_inverse(sK1),sK13(sK1,empty_set)),X0) ),
inference(light_normalisation,[status(thm)],[c_52018,c_4013]) ).
tcf(c_52170,plain,
( in(ordered_pair(apply(sK2,sK24(sK1,empty_set)),sK24(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(sK1,empty_set),relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_52006,c_107]) ).
tcf(c_52171,plain,
( in(ordered_pair(sK24(sK1,empty_set),apply(sK2,sK24(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52006,c_31806]) ).
tcf(c_52172,plain,
( in(ordered_pair(sK24(sK1,empty_set),apply(sK2,sK24(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52171,c_39295]) ).
tcf(c_52175,plain,
( in(ordered_pair(apply(sK2,sK24(sK1,empty_set)),sK24(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_52170,c_3845]) ).
tcf(c_52176,plain,
( in(ordered_pair(apply(sK2,sK24(sK1,empty_set)),sK24(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52175,c_39295]) ).
tcf(c_52219,plain,
( ( sK15(relation_inverse(sK2),sK22(empty_set,sK1)) = apply(sK2,sK22(empty_set,sK1)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42484]) ).
tcf(c_52221,plain,
sK15(relation_inverse(sK2),sK22(empty_set,sK1)) = apply(sK2,sK22(empty_set,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_52219,c_61]) ).
tcf(c_52222,plain,
( in(ordered_pair(apply(sK2,sK22(empty_set,sK1)),sK22(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK22(empty_set,sK1),relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_52221,c_107]) ).
tcf(c_52223,plain,
( in(ordered_pair(sK22(empty_set,sK1),apply(sK2,sK22(empty_set,sK1))),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52221,c_31806]) ).
tcf(c_52224,plain,
( in(ordered_pair(sK22(empty_set,sK1),apply(sK2,sK22(empty_set,sK1))),sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52223,c_40094]) ).
tcf(c_52227,plain,
( in(ordered_pair(apply(sK2,sK22(empty_set,sK1)),sK22(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_52222,c_3845]) ).
tcf(c_52228,plain,
( in(ordered_pair(apply(sK2,sK22(empty_set,sK1)),sK22(empty_set,sK1)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52227,c_40094]) ).
tcf(c_52235,plain,
( ( sK15(relation_inverse(sK2),sK21(sK1,empty_set)) = apply(sK2,sK21(sK1,empty_set)) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_123,c_42485]) ).
tcf(c_52237,plain,
sK15(relation_inverse(sK2),sK21(sK1,empty_set)) = apply(sK2,sK21(sK1,empty_set)),
inference(forward_subsumption_resolution,[status(thm)],[c_52235,c_61]) ).
tcf(c_52238,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,empty_set)),sK21(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK21(sK1,empty_set),relation_rng(relation_inverse(sK2))) ),
inference(superposition,[status(thm)],[c_52237,c_107]) ).
tcf(c_52239,plain,
( in(ordered_pair(sK21(sK1,empty_set),apply(sK2,sK21(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52237,c_31806]) ).
tcf(c_52240,plain,
( in(ordered_pair(sK21(sK1,empty_set),apply(sK2,sK21(sK1,empty_set))),sK2)
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52239,c_39669]) ).
tcf(c_52243,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,empty_set)),sK21(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_52238,c_3845]) ).
tcf(c_52244,plain,
( in(ordered_pair(apply(sK2,sK21(sK1,empty_set)),sK21(sK1,empty_set)),relation_inverse(sK2))
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52243,c_39669]) ).
tcf(c_52274,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34314,c_4044]) ).
tcf(c_52315,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_32119,c_4044]) ).
tcf(c_52317,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40617,c_4044]) ).
tcf(c_52318,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_39295,c_4044]) ).
tcf(c_52319,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40094,c_4044]) ).
tcf(c_52320,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,empty_set))) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_39669,c_4044]) ).
tcf(c_52357,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK5(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_33222,c_4044]) ).
tcf(c_52361,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK22(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_40787,c_4044]) ).
tcf(c_52382,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(sK19(relation_dom(sK2))))) = sK20(sK19(relation_dom(sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52360,c_31365]) ).
tcf(c_53441,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK2,X0),X0,sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_52427,c_49]) ).
tcf(c_53442,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(sK1,apply(sK2,X0))) = apply(sK2,X0) )
| ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(sK2,X0),X1) ),
inference(superposition,[status(thm)],[c_52427,c_53]) ).
tcf(c_53443,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(sK2,X0)),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(sK2,X0),X1) ),
inference(superposition,[status(thm)],[c_52427,c_52]) ).
tcf(c_53475,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(sK2,X0)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK2,X0),relation_dom(sK1))
| ~ sP0(sK1,X0,apply(sK2,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_53443,c_4013]) ).
tcf(c_53600,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = X0 )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89,c_4997]) ).
tcf(c_53601,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,apply(sK2,X0))) = apply(sK2,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_4045,c_4997]) ).
tcf(c_53602,plain,
! [X0: $i] :
( in(sK5(relation_dom(sK1),X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_dom(sK1)) = X0 )
| ( apply(sK2,apply(sK1,ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)))) = ordered_pair(sK5(relation_dom(sK1),X0),sK6(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_77,c_4997]) ).
tcf(c_53603,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(X0,sK7(relation_dom(sK1),X0)))) = ordered_pair(X0,sK7(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_79,c_4997]) ).
tcf(c_53604,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(X0,apply(relation_dom(sK1),X0)))) = ordered_pair(X0,apply(relation_dom(sK1),X0)) )
| ~ function(relation_dom(sK1))
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_dom(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_87,c_4997]) ).
tcf(c_53605,plain,
! [X0: $i] :
( in(sK13(relation_dom(sK1),X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_dom(sK1)) = X0 )
| ( apply(sK2,apply(sK1,ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)))) = ordered_pair(sK14(relation_dom(sK1),X0),sK13(relation_dom(sK1),X0)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_105,c_4997]) ).
tcf(c_53606,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK15(relation_dom(sK1),X0),X0))) = ordered_pair(sK15(relation_dom(sK1),X0),X0) )
| ~ relation(relation_dom(sK1))
| ~ in(X0,relation_rng(relation_dom(sK1))) ),
inference(superposition,[status(thm)],[c_107,c_4997]) ).
tcf(c_53607,plain,
! [X0: $i] :
( in(ordered_pair(sK21(relation_dom(sK1),X0),sK22(relation_dom(sK1),X0)),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = X0 )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)))) = ordered_pair(sK22(relation_dom(sK1),X0),sK21(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4997]) ).
tcf(c_53608,plain,
! [X0: $i] :
( in(ordered_pair(sK22(X0,relation_dom(sK1)),sK21(X0,relation_dom(sK1))),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))))) = ordered_pair(sK21(X0,relation_dom(sK1)),sK22(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_125,c_4997]) ).
tcf(c_53609,plain,
! [X0: $i] :
( in(ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))))) = ordered_pair(sK23(X0,relation_dom(sK1)),sK24(X0,relation_dom(sK1))) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4997]) ).
tcf(c_53610,plain,
! [X0: $i] :
( in(ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)))) = ordered_pair(sK23(relation_dom(sK1),X0),sK24(relation_dom(sK1),X0)) )
| ~ relation(X0)
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_130,c_4997]) ).
tcf(c_53611,plain,
( empty(relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_3448,c_4997]) ).
tcf(c_53612,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK2,apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34571,c_4997]) ).
tcf(c_53618,plain,
( element(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8430,c_4997]) ).
tcf(c_53619,plain,
( element(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_6336,c_4997]) ).
tcf(c_53620,plain,
( in(sK14(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8298,c_4997]) ).
tcf(c_53621,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5563,c_4997]) ).
tcf(c_53622,plain,
( in(sK13(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = sK13(sK1,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_5542,c_4997]) ).
tcf(c_53623,plain,
( in(sK23(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8327,c_4997]) ).
tcf(c_53624,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(relation_dom(sK1),sK1)) = sK23(relation_dom(sK1),sK1) )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5709,c_4997]) ).
tcf(c_53625,plain,
( in(sK24(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)))) = ordered_pair(sK23(relation_dom(sK1),sK1),sK24(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5669,c_4997]) ).
tcf(c_53626,plain,
( in(sK23(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8322,c_4997]) ).
tcf(c_53627,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK24(sK1,relation_dom(sK1))) = sK23(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5704,c_4997]) ).
tcf(c_53628,plain,
( in(sK24(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))))) = ordered_pair(sK23(sK1,relation_dom(sK1)),sK24(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5654,c_4997]) ).
tcf(c_53629,plain,
( in(sK21(relation_dom(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8332,c_4997]) ).
tcf(c_53630,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(relation_inverse(sK1),sK22(relation_dom(sK1),sK1)) = sK21(relation_dom(sK1),sK1) )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5969,c_4997]) ).
tcf(c_53631,plain,
( in(sK22(relation_dom(sK1),sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = sK1 )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)))) = ordered_pair(sK22(relation_dom(sK1),sK1),sK21(relation_dom(sK1),sK1)) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5929,c_4997]) ).
tcf(c_53632,plain,
( in(sK22(sK1,relation_dom(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_8337,c_4997]) ).
tcf(c_53633,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(relation_inverse(sK1),sK21(sK1,relation_dom(sK1))) = sK22(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5964,c_4997]) ).
tcf(c_53634,plain,
( in(sK21(sK1,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_inverse(sK1) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))))) = ordered_pair(sK21(sK1,relation_dom(sK1)),sK22(sK1,relation_dom(sK1))) )
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5914,c_4997]) ).
tcf(c_53635,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8318,c_4997]) ).
tcf(c_53636,plain,
( in(sK22(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_9090,c_4997]) ).
tcf(c_53637,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_8314,c_4997]) ).
tcf(c_53638,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = empty_set )
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8158,c_4997]) ).
tcf(c_53639,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = empty_set )
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_8154,c_4997]) ).
tcf(c_53640,plain,
! [X0: $i] :
( element(sK5(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8540,c_4997]) ).
tcf(c_53641,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8541,c_4997]) ).
tcf(c_53642,plain,
! [X0: $i] :
( in(sK5(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK2,apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8302,c_4997]) ).
tcf(c_53643,plain,
! [X0: $i] :
( element(sK13(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8422,c_4997]) ).
tcf(c_53644,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_8423,c_4997]) ).
tcf(c_53645,plain,
! [X0: $i] :
( in(sK13(sK1,X0),X0)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_8298,c_4997]) ).
tcf(c_53646,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK15(sK1,X0))) = sK15(sK1,X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8294,c_4997]) ).
tcf(c_53647,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = X0 )
| ( apply(sK2,apply(sK1,sK22(sK1,X0))) = sK22(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38316,c_4997]) ).
tcf(c_53648,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_38279,c_4997]) ).
tcf(c_53649,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33869,c_4997]) ).
tcf(c_53650,plain,
! [X0: $i] :
( ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_33839,c_4997]) ).
tcf(c_53651,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,empty_set))) = sK14(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8427,c_4997]) ).
tcf(c_53652,plain,
( in(sK23(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23755,c_4997]) ).
tcf(c_53653,plain,
( in(sK24(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))))) = ordered_pair(sK23(sK2,relation_dom(sK1)),sK24(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18823,c_4997]) ).
tcf(c_53654,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_32739,c_4997]) ).
tcf(c_53655,plain,
( ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_8873,c_4997]) ).
tcf(c_53656,plain,
( ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_8992,c_4997]) ).
tcf(c_53657,plain,
( ( sK1 = empty_set )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_9083,c_4997]) ).
tcf(c_53658,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_40653,c_4997]) ).
tcf(c_53659,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) ) ),
inference(superposition,[status(thm)],[c_34011,c_4997]) ).
tcf(c_53660,plain,
( in(sK5(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23714,c_4997]) ).
tcf(c_53661,plain,
( in(sK6(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK5(sK2,relation_dom(sK1)))) = sK5(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18773,c_4997]) ).
tcf(c_53662,plain,
( in(sK14(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_4997]) ).
tcf(c_53663,plain,
( in(sK13(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK1)))) = sK13(sK2,relation_dom(sK1)) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_4997]) ).
tcf(c_53664,plain,
( in(sK22(sK2,relation_dom(sK1)),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23773,c_4997]) ).
tcf(c_53665,plain,
( in(sK21(sK2,relation_dom(sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_inverse(sK2) )
| ( apply(sK2,apply(sK1,ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))))) = ordered_pair(sK21(sK2,relation_dom(sK1)),sK22(sK2,relation_dom(sK1))) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18841,c_4997]) ).
tcf(c_53666,plain,
( in(sK21(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23767,c_4997]) ).
tcf(c_53667,plain,
( in(sK22(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_dom(sK1)) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)))) = ordered_pair(sK22(relation_dom(sK1),sK2),sK21(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18835,c_4997]) ).
tcf(c_53668,plain,
( in(sK23(relation_dom(sK1),sK2),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_23761,c_4997]) ).
tcf(c_53669,plain,
( in(sK24(relation_dom(sK1),sK2),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = sK2 )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)))) = ordered_pair(sK23(relation_dom(sK1),sK2),sK24(relation_dom(sK1),sK2)) )
| ~ relation(relation_inverse(sK2))
| ~ relation(relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_18829,c_4997]) ).
tcf(c_53670,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_dom(X0)))) = sK5(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29856,c_4997]) ).
tcf(c_53671,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_dom(X0)))) = sK14(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_29866,c_4997]) ).
tcf(c_53672,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_rng(X0)))) = sK5(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30436,c_4997]) ).
tcf(c_53673,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_rng(X0)))) = sK14(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_30444,c_4997]) ).
tcf(c_53674,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK9) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_rng(sK9)))) = sK5(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32144,c_4997]) ).
tcf(c_53675,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK9) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_rng(sK9)))) = sK14(sK1,relation_rng(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_32147,c_4997]) ).
tcf(c_53676,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32763,c_4997]) ).
tcf(c_53677,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32768,c_4997]) ).
tcf(c_53678,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32993,c_4997]) ).
tcf(c_53679,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_inverse(sK12)) ),
inference(superposition,[status(thm)],[c_32997,c_4997]) ).
tcf(c_53680,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK9) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_dom(sK9)))) = sK5(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33532,c_4997]) ).
tcf(c_53681,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK9) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_dom(sK9)))) = sK14(sK1,relation_dom(sK9)) )
| ~ empty(relation_inverse(sK9)) ),
inference(superposition,[status(thm)],[c_33537,c_4997]) ).
tcf(c_53682,plain,
( empty(relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_36111,c_4997]) ).
tcf(c_53683,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_39513,c_4997]) ).
tcf(c_53684,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_39897,c_4997]) ).
tcf(c_53685,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_40406,c_4997]) ).
tcf(c_53686,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_40761,c_4997]) ).
tcf(c_53691,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53611,c_31369]) ).
tcf(c_53694,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_53686,c_40627]) ).
tcf(c_53697,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_53685,c_40105]) ).
tcf(c_53700,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_53684,c_39713]) ).
tcf(c_53703,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_53683,c_39305]) ).
tcf(c_53715,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53682,c_31369]) ).
tcf(c_53757,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = X0 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53600,c_65,c_64]) ).
tcf(c_54400,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12791,c_53757]) ).
tcf(c_54401,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK2,X0) = sK15(sK1,X0) )
| ( apply(sK1,sK15(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_13464,c_53757]) ).
tcf(c_54402,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = apply(sK2,empty_set) )
| ( apply(relation_inverse(sK1),X0) = sK7(relation_inverse(sK1),X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10494,c_53757]) ).
tcf(c_54403,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10201,c_53757]) ).
tcf(c_54404,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( sK7(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_10244,c_53757]) ).
tcf(c_54405,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33899,c_53757]) ).
tcf(c_54406,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10207,c_53757]) ).
tcf(c_54407,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10226,c_53757]) ).
tcf(c_54408,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK7(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10228,c_53757]) ).
tcf(c_54409,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = apply(sK2,sK6(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32125,c_53757]) ).
tcf(c_54410,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK13(sK1,empty_set)) = apply(sK2,sK13(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_10231,c_53757]) ).
tcf(c_54411,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12764,c_53757]) ).
tcf(c_54412,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(relation_inverse(sK1),X0) = apply(sK2,X0) )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_12807,c_53757]) ).
tcf(c_54413,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = apply(sK2,sK5(sK1,relation_dom(sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12770,c_53757]) ).
tcf(c_54414,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12789,c_53757]) ).
tcf(c_54415,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,empty_set)) = apply(sK2,sK13(sK1,empty_set)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_12794,c_53757]) ).
tcf(c_54416,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34151,c_53757]) ).
tcf(c_54417,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = apply(sK2,sK24(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39302,c_53757]) ).
tcf(c_54418,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = apply(sK2,sK24(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40624,c_53757]) ).
tcf(c_54419,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = apply(sK2,apply(sK1,sK5(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33228,c_53757]) ).
tcf(c_54420,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = apply(sK2,sK21(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39676,c_53757]) ).
tcf(c_54422,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = apply(sK2,sK22(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40100,c_53757]) ).
tcf(c_54424,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = apply(sK2,apply(sK1,sK22(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40793,c_53757]) ).
tcf(c_54425,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK1,X0),X0,sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_53757,c_49]) ).
tcf(c_54426,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK2,apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(sK2,X0,apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_53757,c_53]) ).
tcf(c_54427,plain,
! [X0: $i,X1: $i] :
( in(apply(sK2,apply(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(sK2,X0,apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_53757,c_52]) ).
tcf(c_54428,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK1,X0)),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK2,apply(sK1,X0)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_53757,c_53470]) ).
tcf(c_54429,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),X0)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_53757,c_19430]) ).
tcf(c_54430,plain,
! [X0: $i] :
( in(X0,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_53757,c_4045]) ).
tcf(c_54431,plain,
! [X0: $i] :
( element(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_53757,c_19431]) ).
tcf(c_54432,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_53757,c_18734]) ).
tcf(c_54433,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_53757,c_87]) ).
tcf(c_54457,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(sK2,sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(light_normalisation,[status(thm)],[c_54416,c_34151]) ).
tcf(c_54465,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = apply(sK2,sK22(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_54422,c_40100]) ).
tcf(c_54469,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = apply(sK2,sK21(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_54420,c_39676]) ).
tcf(c_54473,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = apply(sK2,sK24(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_54418,c_40624]) ).
tcf(c_54477,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = apply(sK2,sK24(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_54417,c_39302]) ).
tcf(c_54485,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = apply(sK2,sK6(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_54409,c_32125]) ).
tcf(c_54489,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = apply(sK2,sK20(relation_dom(sK2))) ) ),
inference(light_normalisation,[status(thm)],[c_54405,c_33899]) ).
tcf(c_54505,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),X0),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54433,c_62,c_61]) ).
tcf(c_54528,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = apply(sK2,apply(sK1,sK22(sK1,empty_set))) ) ),
inference(light_normalisation,[status(thm)],[c_54424,c_40793]) ).
tcf(c_54532,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = apply(sK2,apply(sK1,sK5(sK1,empty_set))) ) ),
inference(light_normalisation,[status(thm)],[c_54419,c_33228]) ).
tcf(c_54629,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(sK2,X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(apply(sK1,apply(sK2,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52427,c_54505]) ).
tcf(c_54630,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),apply(sK2,sK20(relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(sK2,sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8695,c_54505]) ).
tcf(c_54631,plain,
( in(ordered_pair(sK21(sK1,sK1),apply(relation_inverse(sK1),sK21(sK1,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12791,c_54505]) ).
tcf(c_54632,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK15(sK1,X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13464,c_54505]) ).
tcf(c_54634,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(relation_inverse(sK1),X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10201,c_54505]) ).
tcf(c_54635,plain,
! [X0: $i] :
( in(ordered_pair(X0,sK7(relation_inverse(sK1),X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10244,c_54505]) ).
tcf(c_54636,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33899,c_54505]) ).
tcf(c_54637,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10207,c_54505]) ).
tcf(c_54638,plain,
( in(ordered_pair(sK22(sK1,sK1),sK7(relation_inverse(sK1),sK22(sK1,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10226,c_54505]) ).
tcf(c_54639,plain,
( in(ordered_pair(sK21(sK1,sK1),sK7(relation_inverse(sK1),sK21(sK1,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10228,c_54505]) ).
tcf(c_54640,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32125,c_54505]) ).
tcf(c_54641,plain,
( in(ordered_pair(sK13(sK1,empty_set),sK7(relation_inverse(sK1),sK13(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10231,c_54505]) ).
tcf(c_54642,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12764,c_54505]) ).
tcf(c_54643,plain,
! [X0: $i] :
( in(ordered_pair(X0,apply(relation_inverse(sK1),X0)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12807,c_54505]) ).
tcf(c_54644,plain,
( in(ordered_pair(sK5(sK1,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12770,c_54505]) ).
tcf(c_54645,plain,
( in(ordered_pair(sK22(sK1,sK1),apply(relation_inverse(sK1),sK22(sK1,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12789,c_54505]) ).
tcf(c_54646,plain,
( in(ordered_pair(sK13(sK1,empty_set),apply(relation_inverse(sK1),sK13(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12794,c_54505]) ).
tcf(c_54647,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_34151,c_54505]) ).
tcf(c_54648,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39302,c_54505]) ).
tcf(c_54649,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40624,c_54505]) ).
tcf(c_54650,plain,
( in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33228,c_54505]) ).
tcf(c_54651,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39676,c_54505]) ).
tcf(c_54652,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39713,c_54505]) ).
tcf(c_54653,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40100,c_54505]) ).
tcf(c_54654,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40105,c_54505]) ).
tcf(c_54655,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40793,c_54505]) ).
tcf(c_54656,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ in(sK2,ordered_pair(apply(sK1,X0),X0)) ),
inference(superposition,[status(thm)],[c_54505,c_70]) ).
tcf(c_54657,plain,
! [X0: $i] :
( element(ordered_pair(apply(sK1,X0),X0),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_54505,c_69]) ).
tcf(c_54659,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ relation(sK2)
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_54505,c_106]) ).
tcf(c_54662,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ~ relation(sK2)
| ~ in(sK13(sK2,X0),X0)
| ~ in(apply(sK1,sK13(sK2,X0)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_54505,c_104]) ).
tcf(c_54665,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54659,c_61]) ).
tcf(c_54688,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ~ in(sK13(sK2,X0),X0)
| ~ in(apply(sK1,sK13(sK2,X0)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54662,c_61]) ).
tcf(c_54694,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54654,c_40105]) ).
tcf(c_54695,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK15(sK1,sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54694,c_40094]) ).
tcf(c_54699,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54652,c_39713]) ).
tcf(c_54700,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK15(sK1,sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54699,c_39669]) ).
tcf(c_54704,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54647,c_34151]) ).
tcf(c_54733,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54653,c_40100]) ).
tcf(c_54734,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54733,c_40094]) ).
tcf(c_54738,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54651,c_39676]) ).
tcf(c_54739,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54738,c_39669]) ).
tcf(c_54743,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54649,c_40624]) ).
tcf(c_54744,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54743,c_40617]) ).
tcf(c_54748,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54648,c_39302]) ).
tcf(c_54749,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54748,c_39295]) ).
tcf(c_54753,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54640,c_32125]) ).
tcf(c_54754,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54753,c_32119]) ).
tcf(c_54758,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54636,c_33899]) ).
tcf(c_54773,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54655,c_40793]) ).
tcf(c_54774,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54773,c_40787]) ).
tcf(c_54778,plain,
( in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54650,c_33228]) ).
tcf(c_54779,plain,
( in(ordered_pair(apply(sK1,sK5(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54778,c_33222]) ).
tcf(c_54924,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ function(sK2)
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89,c_54665]) ).
tcf(c_54926,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_54665]) ).
tcf(c_54927,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ~ in(X0,relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_54665]) ).
tcf(c_54928,plain,
( in(sK5(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_33222,c_54665]) ).
tcf(c_54929,plain,
( in(sK22(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_40787,c_54665]) ).
tcf(c_54930,plain,
! [X0: $i] :
( in(apply(sK2,X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(sK2,X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_52427,c_54665]) ).
tcf(c_54931,plain,
( in(apply(sK2,sK20(relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_8695,c_54665]) ).
tcf(c_54932,plain,
( in(apply(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12791,c_54665]) ).
tcf(c_54933,plain,
! [X0: $i] :
( in(sK15(sK1,X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK15(sK1,X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13464,c_54665]) ).
tcf(c_54935,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10201,c_54665]) ).
tcf(c_54936,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10244,c_54665]) ).
tcf(c_54937,plain,
( in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33899,c_54665]) ).
tcf(c_54938,plain,
( in(sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10207,c_54665]) ).
tcf(c_54939,plain,
( in(sK7(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10226,c_54665]) ).
tcf(c_54940,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = empty_set )
| ~ in(sK21(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10228,c_54665]) ).
tcf(c_54941,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32125,c_54665]) ).
tcf(c_54942,plain,
( in(sK7(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10231,c_54665]) ).
tcf(c_54943,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12764,c_54665]) ).
tcf(c_54944,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12807,c_54665]) ).
tcf(c_54945,plain,
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12770,c_54665]) ).
tcf(c_54946,plain,
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12789,c_54665]) ).
tcf(c_54947,plain,
( in(apply(relation_inverse(sK1),sK13(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(sK1,empty_set))) = empty_set )
| ~ in(sK13(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12794,c_54665]) ).
tcf(c_54948,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_34151,c_54665]) ).
tcf(c_54949,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39302,c_54665]) ).
tcf(c_54950,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40624,c_54665]) ).
tcf(c_54951,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33228,c_54665]) ).
tcf(c_54952,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39676,c_54665]) ).
tcf(c_54953,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39713,c_54665]) ).
tcf(c_54954,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40100,c_54665]) ).
tcf(c_54955,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40105,c_54665]) ).
tcf(c_54956,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40793,c_54665]) ).
tcf(c_54971,plain,
! [X0: $i] :
( in(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54924,c_62,c_61]) ).
tcf(c_54976,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54955,c_40105]) ).
tcf(c_54977,plain,
( in(sK15(sK1,sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54976,c_40094]) ).
tcf(c_54981,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54953,c_39713]) ).
tcf(c_54982,plain,
( in(sK15(sK1,sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_54981,c_39669]) ).
tcf(c_54986,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54948,c_34151]) ).
tcf(c_55005,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54954,c_40100]) ).
tcf(c_55006,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55005,c_40094]) ).
tcf(c_55010,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54952,c_39676]) ).
tcf(c_55011,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55010,c_39669]) ).
tcf(c_55015,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54950,c_40624]) ).
tcf(c_55016,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55015,c_40617]) ).
tcf(c_55020,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54949,c_39302]) ).
tcf(c_55021,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55020,c_39295]) ).
tcf(c_55030,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54941,c_32125]) ).
tcf(c_55031,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55030,c_32119]) ).
tcf(c_55035,plain,
( in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54937,c_33899]) ).
tcf(c_55065,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54956,c_40793]) ).
tcf(c_55066,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55065,c_40787]) ).
tcf(c_55070,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_54951,c_33228]) ).
tcf(c_55071,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55070,c_33222]) ).
tcf(c_55224,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(relation_rng(sK2),X0) ),
inference(superposition,[status(thm)],[c_54971,c_70]) ).
tcf(c_55225,plain,
! [X0: $i] :
( element(X0,relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_69]) ).
tcf(c_55227,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(relation_rng(sK2)) = X0 )
| ( apply(sK1,ordered_pair(sK5(relation_rng(sK2),X0),X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK5(relation_rng(sK2),X0),X1))) = empty_set )
| ~ relation(relation_rng(sK2))
| ~ in(sK5(relation_rng(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_54971,c_76]) ).
tcf(c_55228,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(relation_rng(sK2)))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_54971,c_106]) ).
tcf(c_55229,plain,
! [X0: $i,X1: $i] :
( in(X0,relation_dom(relation_rng(sK2)))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_54971,c_78]) ).
tcf(c_55230,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_rng(sK2),X0) = X1 )
| ( apply(sK1,ordered_pair(X0,X1)) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X0,X1))) = empty_set )
| ~ function(relation_rng(sK2))
| ~ relation(relation_rng(sK2)) ),
inference(superposition,[status(thm)],[c_54971,c_197]) ).
tcf(c_55231,plain,
! [X0: $i,X1: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(relation_rng(sK2)) = X0 )
| ( apply(sK1,ordered_pair(X1,sK13(relation_rng(sK2),X0))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(X1,sK13(relation_rng(sK2),X0)))) = empty_set )
| ~ relation(relation_rng(sK2))
| ~ in(sK13(relation_rng(sK2),X0),X0) ),
inference(superposition,[status(thm)],[c_54971,c_104]) ).
tcf(c_55232,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(relation_rng(sK2)) = X0 )
| ( apply(sK1,ordered_pair(sK22(relation_rng(sK2),X0),sK21(relation_rng(sK2),X0))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK22(relation_rng(sK2),X0),sK21(relation_rng(sK2),X0)))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_rng(sK2))
| ~ in(ordered_pair(sK21(relation_rng(sK2),X0),sK22(relation_rng(sK2),X0)),X0) ),
inference(superposition,[status(thm)],[c_54971,c_124]) ).
tcf(c_55233,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))))) = empty_set )
| ~ relation(X0)
| ~ relation(relation_rng(sK2))
| ~ in(ordered_pair(sK23(X0,relation_rng(sK2)),sK24(X0,relation_rng(sK2))),X0) ),
inference(superposition,[status(thm)],[c_54971,c_129]) ).
tcf(c_55234,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),X0)) = X0 )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_54971,c_43161]) ).
tcf(c_55235,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_rng(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_12622]) ).
tcf(c_55236,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(sK1,sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_rng(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_10578]) ).
tcf(c_55237,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK5(sK2,relation_rng(sK2))) = empty_set )
| ( apply(sK1,sK5(sK2,relation_rng(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK2,relation_rng(sK2)))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_54971,c_43088]) ).
tcf(c_55238,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ relation(relation_inverse(sK2))
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_54971,c_43165]) ).
tcf(c_55347,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_89,c_54688]) ).
tcf(c_55348,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ( apply(sK1,sK15(sK1,apply(sK1,sK13(sK2,X0)))) = empty_set )
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_38509,c_54688]) ).
tcf(c_55349,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ in(sK13(sK2,X0),X0) ),
inference(superposition,[status(thm)],[c_4546,c_54688]) ).
tcf(c_55350,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ~ in(sK13(sK2,X0),X0)
| ~ in(sK13(sK2,X0),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_5332,c_54688]) ).
tcf(c_55361,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ in(sK13(sK2,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_55347,c_62,c_61]) ).
tcf(c_55667,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = relation_rng(sK2) )
| ( apply(sK1,sK13(sK2,relation_dom(X0))) = empty_set )
| ( apply(X0,sK13(sK2,relation_dom(X0))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(X0)))) = empty_set )
| ~ function(X0)
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_89,c_55361]) ).
tcf(c_55668,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK2,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK13(sK2,relation_dom(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK2)))) = empty_set )
| ( apply(sK1,sK15(sK1,sK13(sK2,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_38509,c_55361]) ).
tcf(c_55669,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK2,relation_dom(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK2,relation_dom(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_4546,c_55361]) ).
tcf(c_55671,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_rng(sK12) )
| ( apply(sK1,sK13(sK2,relation_rng(sK12))) = empty_set )
| ( apply(relation_inverse(sK12),sK13(sK2,relation_rng(sK12))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_rng(sK12)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_5420,c_55361]) ).
tcf(c_55672,plain,
! [X0: $i] :
( in(sK14(sK2,X0),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_23709,c_55361]) ).
tcf(c_55673,plain,
! [X0: $i] :
( in(sK13(sK2,X0),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = X0 )
| ( apply(sK1,sK13(sK2,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,X0))) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_18768,c_55361]) ).
tcf(c_55777,plain,
apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = sK15(sK1,sK7(sK1,sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_32739,c_5349]) ).
tcf(c_55781,plain,
apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = sK15(sK1,sK7(sK1,sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40653,c_5349]) ).
tcf(c_55806,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39513,c_5349]) ).
tcf(c_55807,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39897,c_5349]) ).
tcf(c_55808,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40406,c_5349]) ).
tcf(c_55809,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40761,c_5349]) ).
tcf(c_55810,plain,
sK15(sK1,sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_55781,c_40661]) ).
tcf(c_55811,plain,
sK15(sK1,sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_55777,c_32746]) ).
tcf(c_55812,plain,
( empty(relation_dom(sK1))
| ( sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_55734,c_31958]) ).
tcf(c_55813,plain,
sK15(sK1,sK7(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_55812,c_31369]) ).
tcf(c_55814,plain,
sK15(sK1,sK7(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,sK24(empty_set,sK1)),
inference(light_normalisation,[status(thm)],[c_55809,c_40768]) ).
tcf(c_55815,plain,
sK15(sK1,sK7(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,sK22(empty_set,sK1)),
inference(light_normalisation,[status(thm)],[c_55808,c_40613]) ).
tcf(c_55816,plain,
sK15(sK1,sK7(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,sK21(sK1,empty_set)),
inference(light_normalisation,[status(thm)],[c_55807,c_39942]) ).
tcf(c_55817,plain,
sK15(sK1,sK7(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,sK24(sK1,empty_set)),
inference(light_normalisation,[status(thm)],[c_55806,c_39520]) ).
tcf(c_55818,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_55780,c_41530]) ).
tcf(c_55821,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_55779,c_41403]) ).
tcf(c_55824,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_55778,c_40987]) ).
tcf(c_55827,plain,
( empty(relation_dom(sK1))
| ( sK15(sK1,sK7(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_55805,c_36543]) ).
tcf(c_55828,plain,
sK15(sK1,sK7(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_55827,c_31369]) ).
tcf(c_56200,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(sK1,X0),sK15(sK1,sK7(sK1,X0)),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_55855,c_49]) ).
tcf(c_56201,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_55855,c_53]) ).
tcf(c_56202,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_55855,c_52]) ).
tcf(c_56219,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_55855,c_40987]) ).
tcf(c_56220,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_55855,c_41403]) ).
tcf(c_56221,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_55855,c_41530]) ).
tcf(c_56279,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_56202,c_3821,c_4030]) ).
tcf(c_56284,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,X0))) = sK7(sK1,X0) )
| ~ in(sK7(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_56201,c_4030]) ).
tcf(c_56497,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_56474,c_4997]) ).
tcf(c_56507,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK13(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK2,sK7(sK1,sK13(sK2,relation_dom(sK1)))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_55361]) ).
tcf(c_56508,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,sK7(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_34158]) ).
tcf(c_56509,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,sK7(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_56474,c_33908]) ).
tcf(c_56678,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,empty_set)))) = sK15(sK1,apply(sK1,sK15(sK1,sK24(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39513,c_6249]) ).
tcf(c_56679,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,empty_set)))) = sK15(sK1,apply(sK1,sK15(sK1,sK21(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_39897,c_6249]) ).
tcf(c_56680,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(empty_set,sK1)))) = sK15(sK1,apply(sK1,sK15(sK1,sK22(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40406,c_6249]) ).
tcf(c_56681,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(empty_set,sK1)))) = sK15(sK1,apply(sK1,sK15(sK1,sK24(empty_set,sK1)))),
inference(superposition,[status(thm)],[c_40761,c_6249]) ).
tcf(c_56682,plain,
( empty(relation_dom(sK1))
| ( sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_56606,c_32039]) ).
tcf(c_56683,plain,
sK15(sK1,apply(sK1,sK20(relation_dom(sK1)))) = sK20(relation_dom(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_56682,c_31369]) ).
tcf(c_56688,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_56652,c_41474]) ).
tcf(c_56691,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_56651,c_41214]) ).
tcf(c_56694,plain,
( ( sK1 = empty_set )
| ( sK15(sK1,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_56650,c_40931]) ).
tcf(c_56697,plain,
( empty(relation_dom(sK1))
| ( sK15(sK1,apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_56677,c_36544]) ).
tcf(c_56698,plain,
sK15(sK1,apply(sK1,sK20(sK19(relation_dom(sK1))))) = sK20(sK19(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_56697,c_31369]) ).
tcf(c_57175,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33228,c_56725]) ).
tcf(c_57180,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40793,c_56725]) ).
tcf(c_57181,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK1,X0),sK15(sK1,apply(sK1,X0)),relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_56725,c_49]) ).
tcf(c_57182,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,apply(sK1,X0)),apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_56725,c_53]) ).
tcf(c_57183,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_rng(relation_inverse(sK1)))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,apply(sK1,X0)),apply(sK1,X0),X1) ),
inference(superposition,[status(thm)],[c_56725,c_52]) ).
tcf(c_57200,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ( sK15(sK1,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_56725,c_40931]) ).
tcf(c_57201,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ( sK15(sK1,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_56725,c_41214]) ).
tcf(c_57202,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( sK15(sK1,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_56725,c_41474]) ).
tcf(c_57262,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,apply(sK1,X0)),apply(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_57183,c_3821,c_4030]) ).
tcf(c_57267,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,X0))) = apply(sK1,X0) )
| ~ in(apply(sK1,X0),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,apply(sK1,X0)),apply(sK1,X0),X1) ),
inference(light_normalisation,[status(thm)],[c_57182,c_4030]) ).
tcf(c_57555,plain,
sK15(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1))) = apply(sK1,sK13(empty_set,relation_dom(sK1))),
inference(global_subsumption_just,[status(thm)],[c_13377,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_13377,c_16946,c_19508,c_30801]) ).
tcf(c_57557,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_57555,c_107]) ).
tcf(c_57558,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57555,c_4472]) ).
tcf(c_57561,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_57557,c_3821]) ).
tcf(c_57562,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57561,c_3611]) ).
tcf(c_57788,plain,
( ( sK7(relation_inverse(sK1),sK20(relation_dom(sK2))) = sK15(sK1,sK20(relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33899,c_57193]) ).
tcf(c_57792,plain,
( ( sK7(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_32125,c_57193]) ).
tcf(c_57799,plain,
( ( sK7(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39302,c_57193]) ).
tcf(c_57800,plain,
( ( sK7(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40624,c_57193]) ).
tcf(c_57801,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_33228,c_57193]) ).
tcf(c_57802,plain,
( ( sK7(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set ) ),
inference(superposition,[status(thm)],[c_39676,c_57193]) ).
tcf(c_57803,plain,
( ( sK7(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40100,c_57193]) ).
tcf(c_57804,plain,
( ( sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_40793,c_57193]) ).
tcf(c_57880,plain,
( in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33899,c_57811]) ).
tcf(c_57884,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32125,c_57811]) ).
tcf(c_57891,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_34151,c_57811]) ).
tcf(c_57892,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39302,c_57811]) ).
tcf(c_57893,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40624,c_57811]) ).
tcf(c_57894,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33228,c_57811]) ).
tcf(c_57895,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39676,c_57811]) ).
tcf(c_57897,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40100,c_57811]) ).
tcf(c_57899,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40793,c_57811]) ).
tcf(c_57904,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57891,c_34151]) ).
tcf(c_57912,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57897,c_40100]) ).
tcf(c_57913,plain,
( in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1))
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57912,c_40094]) ).
tcf(c_57916,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57895,c_39676]) ).
tcf(c_57917,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1))
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57916,c_39669]) ).
tcf(c_57920,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57893,c_40624]) ).
tcf(c_57921,plain,
( in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1))
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57920,c_40617]) ).
tcf(c_57924,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57892,c_39302]) ).
tcf(c_57925,plain,
( in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1))
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57924,c_39295]) ).
tcf(c_57932,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57884,c_32125]) ).
tcf(c_57933,plain,
( in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1))
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57932,c_32119]) ).
tcf(c_57936,plain,
( in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1))
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57880,c_33899]) ).
tcf(c_57961,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57899,c_40793]) ).
tcf(c_57962,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57961,c_40787]) ).
tcf(c_57965,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_57894,c_33228]) ).
tcf(c_57966,plain,
( in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1))
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57965,c_33222]) ).
tcf(c_58021,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_57900,c_4997]) ).
tcf(c_58031,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK1) )
| ( apply(sK1,sK13(sK2,relation_dom(sK1))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK2,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_55361]) ).
tcf(c_58032,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_34158]) ).
tcf(c_58033,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_57900,c_33908]) ).
tcf(c_58146,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))) ) ),
inference(superposition,[status(thm)],[c_34314,c_8395]) ).
tcf(c_58187,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK6(sK1,empty_set)))) = sK15(sK1,sK6(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32119,c_8395]) ).
tcf(c_58229,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,apply(sK1,sK5(sK1,empty_set))))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_33222,c_8395]) ).
tcf(c_58233,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,apply(sK1,sK22(sK1,empty_set))))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40787,c_8395]) ).
tcf(c_58240,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2)))))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_58232,c_31365]) ).
tcf(c_58840,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK1,sK15(sK1,X0)),sK15(sK1,X0),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_58270,c_49]) ).
tcf(c_58841,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0)))) = apply(sK1,sK15(sK1,X0)) )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),apply(sK1,sK15(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_58270,c_53]) ).
tcf(c_58842,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),apply(sK1,sK15(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_58270,c_52]) ).
tcf(c_58889,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0))),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),apply(sK1,sK15(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_58842,c_3821,c_4030]) ).
tcf(c_58894,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,X0)))) = apply(sK1,sK15(sK1,X0)) )
| ~ in(apply(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),apply(sK1,sK15(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_58841,c_4030]) ).
tcf(c_59036,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK6(sK1,empty_set)))) = sK15(sK1,sK6(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32119,c_8396]) ).
tcf(c_59078,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,apply(sK1,sK5(sK1,empty_set))))) = sK15(sK1,apply(sK1,sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_33222,c_8396]) ).
tcf(c_59082,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,apply(sK1,sK22(sK1,empty_set))))) = sK15(sK1,apply(sK1,sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_40787,c_8396]) ).
tcf(c_59085,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = sK15(sK1,sK20(relation_dom(sK2))),
inference(forward_subsumption_resolution,[status(thm)],[c_58990,c_31365]) ).
tcf(c_59088,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2)))))) = sK15(sK1,sK20(sK19(relation_dom(sK2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_59081,c_31365]) ).
tcf(c_59700,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(sK1,sK15(sK1,X0)),sK15(sK1,X0),relation_inverse(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_59117,c_49]) ).
tcf(c_59701,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0)))) = sK7(sK1,sK15(sK1,X0)) )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),sK7(sK1,sK15(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_59117,c_53]) ).
tcf(c_59702,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),sK7(sK1,sK15(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_59117,c_52]) ).
tcf(c_59757,plain,
! [X0: $i,X1: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0))),relation_dom(sK1))
| ( apply(sK2,X0) = empty_set )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),sK7(sK1,sK15(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_59702,c_3821,c_4030]) ).
tcf(c_59762,plain,
! [X0: $i,X1: $i] :
( ( apply(sK2,X0) = empty_set )
| ( apply(X1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,X0)))) = sK7(sK1,sK15(sK1,X0)) )
| ~ in(sK7(sK1,sK15(sK1,X0)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,X0),sK7(sK1,sK15(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_59701,c_4030]) ).
tcf(c_59821,plain,
apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_13380,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_13380,c_16946,c_19508,c_30801]) ).
tcf(c_59826,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1)),relation_inverse(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_59821,c_49]) ).
tcf(c_59827,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1))))) = apply(sK1,sK13(empty_set,relation_dom(sK1))) )
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_59821,c_53]) ).
tcf(c_59828,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_59821,c_52]) ).
tcf(c_59829,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_59821,c_87]) ).
tcf(c_59830,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_59821,c_34564]) ).
tcf(c_59831,plain,
( element(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59821,c_34565]) ).
tcf(c_59832,plain,
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59821,c_34571]) ).
tcf(c_59833,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59821,c_34529]) ).
tcf(c_59834,plain,
( ( sK15(sK1,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59821,c_9713]) ).
tcf(c_59835,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59821,c_13488]) ).
tcf(c_59836,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_59821,c_4623]) ).
tcf(c_59837,plain,
( ( sK15(sK1,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_59821,c_4763]) ).
tcf(c_59838,plain,
( ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ( sK15(sK1,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_59821,c_56725]) ).
tcf(c_59839,plain,
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( sK13(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_59832,c_59821]) ).
tcf(c_59850,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( sK13(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_59833,c_59821]) ).
tcf(c_59853,plain,
( element(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( sK13(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_59831,c_59821]) ).
tcf(c_59856,plain,
( ( sK13(empty_set,relation_dom(sK1)) = empty_set )
| ( sK15(sK1,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_59834,c_59821]) ).
tcf(c_59859,plain,
( ( sK13(empty_set,relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_59830,c_59821]) ).
tcf(c_59862,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_59829,c_4030]) ).
tcf(c_59863,plain,
( in(ordered_pair(apply(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_59862,c_987,c_3611]) ).
tcf(c_59866,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_59835,c_59821]) ).
tcf(c_59870,plain,
! [X0: $i] :
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_59828,c_3821,c_4030,c_59821]) ).
tcf(c_59874,plain,
! [X0: $i] :
( ( apply(X0,sK13(empty_set,relation_dom(sK1))) = apply(sK1,sK13(empty_set,relation_dom(sK1))) )
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_59827,c_4030,c_59821]) ).
tcf(c_60208,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set)))) = sK7(sK1,sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32739,c_10202]) ).
tcf(c_60212,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set)))) = sK7(sK1,sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40653,c_10202]) ).
tcf(c_60237,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_10202]) ).
tcf(c_60238,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_10202]) ).
tcf(c_60239,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_10202]) ).
tcf(c_60240,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_10202]) ).
tcf(c_60241,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(relation_dom(sK1))))) = sK7(sK1,sK20(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_60165,c_31369]) ).
tcf(c_60248,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(sK19(relation_dom(sK1)))))) = sK7(sK1,sK20(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_60236,c_31369]) ).
tcf(c_60733,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_60275,c_49]) ).
tcf(c_60734,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0)))) = sK7(relation_inverse(sK1),sK7(sK1,X0)) )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK7(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_60275,c_53]) ).
tcf(c_60735,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK7(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_60275,c_52]) ).
tcf(c_60740,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_60275,c_54665]) ).
tcf(c_60741,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK7(relation_inverse(sK1),sK7(sK1,X0))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_60275,c_54505]) ).
tcf(c_60742,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( sK7(relation_inverse(sK1),sK7(sK1,X0)) = apply(sK2,sK7(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_60275,c_53757]) ).
tcf(c_60790,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK7(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_60735,c_4013]) ).
tcf(c_61094,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,empty_set))))) = apply(sK1,sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_10203]) ).
tcf(c_61095,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,empty_set))))) = apply(sK1,sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_10203]) ).
tcf(c_61096,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(empty_set,sK1))))) = apply(sK1,sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_10203]) ).
tcf(c_61097,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(empty_set,sK1))))) = apply(sK1,sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_10203]) ).
tcf(c_61098,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1))))) = apply(sK1,sK20(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_61022,c_31369]) ).
tcf(c_61109,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(sK19(relation_dom(sK1)))))) = apply(sK1,sK20(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_61093,c_31369]) ).
tcf(c_61539,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_61136,c_49]) ).
tcf(c_61540,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0)))) = sK7(relation_inverse(sK1),apply(sK1,X0)) )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),sK7(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_61136,c_53]) ).
tcf(c_61541,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),sK7(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_61136,c_52]) ).
tcf(c_61546,plain,
! [X0: $i] :
( in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61136,c_54665]) ).
tcf(c_61547,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),sK7(relation_inverse(sK1),apply(sK1,X0))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61136,c_54505]) ).
tcf(c_61548,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( sK7(relation_inverse(sK1),apply(sK1,X0)) = apply(sK2,apply(sK1,X0)) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61136,c_53757]) ).
tcf(c_61603,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),sK7(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_61541,c_4013]) ).
tcf(c_61669,plain,
apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_13381,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_13381,c_16946,c_19508,c_30801]) ).
tcf(c_61674,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_61669,c_49]) ).
tcf(c_61675,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1))))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_61669,c_53]) ).
tcf(c_61676,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_61669,c_52]) ).
tcf(c_61677,plain,
( in(ordered_pair(sK7(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_61669,c_87]) ).
tcf(c_61678,plain,
( ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ( sK15(sK1,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_61669,c_55855]) ).
tcf(c_61679,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_61669,c_34564]) ).
tcf(c_61680,plain,
( element(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_34565]) ).
tcf(c_61681,plain,
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_34571]) ).
tcf(c_61682,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_34529]) ).
tcf(c_61683,plain,
( ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_12764]) ).
tcf(c_61684,plain,
( ( sK15(sK1,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_9713]) ).
tcf(c_61685,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61669,c_13488]) ).
tcf(c_61686,plain,
( ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) )
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_12807]) ).
tcf(c_61687,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61669,c_4623]) ).
tcf(c_61688,plain,
( ( sK15(sK1,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_61669,c_4763]) ).
tcf(c_61700,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( sK13(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_61682,c_61669]) ).
tcf(c_61703,plain,
( element(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( sK13(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_61680,c_61669]) ).
tcf(c_61706,plain,
( ( sK13(empty_set,relation_dom(sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = sK13(empty_set,relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_61684,c_61669]) ).
tcf(c_61709,plain,
( ( sK13(empty_set,relation_dom(sK1)) = empty_set )
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_61683,c_61669]) ).
tcf(c_61712,plain,
( ( sK13(empty_set,relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_61679,c_61669]) ).
tcf(c_61715,plain,
( in(ordered_pair(sK7(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_61677,c_4030]) ).
tcf(c_61716,plain,
( in(ordered_pair(sK7(sK1,sK13(empty_set,relation_dom(sK1))),sK13(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_61715,c_987,c_3611]) ).
tcf(c_61719,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_61685,c_61669]) ).
tcf(c_61723,plain,
! [X0: $i] :
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_61676,c_3821,c_4030,c_61669]) ).
tcf(c_61727,plain,
! [X0: $i] :
( ( apply(X0,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_61675,c_4030,c_61669]) ).
tcf(c_62075,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_61586]) ).
tcf(c_62081,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32125,c_61586]) ).
tcf(c_62088,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_61586]) ).
tcf(c_62089,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39302,c_61586]) ).
tcf(c_62090,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40624,c_61586]) ).
tcf(c_62091,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33228,c_61586]) ).
tcf(c_62092,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39676,c_61586]) ).
tcf(c_62093,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK15(sK1,sK21(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39713,c_61586]) ).
tcf(c_62094,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40100,c_61586]) ).
tcf(c_62095,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40105,c_61586]) ).
tcf(c_62096,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40793,c_61586]) ).
tcf(c_62121,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62095,c_40105]) ).
tcf(c_62125,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62093,c_39713]) ).
tcf(c_62129,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62088,c_34151]) ).
tcf(c_62147,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62090,c_40624]) ).
tcf(c_62151,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62089,c_39302]) ).
tcf(c_62155,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62081,c_32125]) ).
tcf(c_62185,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62096,c_40793]) ).
tcf(c_62189,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_62091,c_33228]) ).
tcf(c_62260,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_62259,c_31365]) ).
tcf(c_62294,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK20(powerset(X0)) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,sK20(powerset(X0))))) = sK5(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11849,c_4997]) ).
tcf(c_62401,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( sK20(powerset(X0)) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,sK20(powerset(X0))))) = sK14(sK1,sK20(powerset(X0))) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_11852,c_4997]) ).
tcf(c_62555,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13383,c_49]) ).
tcf(c_62556,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))) = apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_13383,c_53]) ).
tcf(c_62557,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_13383,c_52]) ).
tcf(c_62564,plain,
( in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13383,c_54665]) ).
tcf(c_62565,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13383,c_54505]) ).
tcf(c_62566,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = apply(sK2,sK13(empty_set,relation_dom(sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13383,c_53757]) ).
tcf(c_62605,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_62557,c_4013]) ).
tcf(c_62732,plain,
( ( sK20(relation_dom(sK2)) = empty_set )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) ) ),
inference(superposition,[status(thm)],[c_34314,c_12335]) ).
tcf(c_62773,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set))) = apply(sK1,sK15(sK1,sK6(sK1,empty_set))),
inference(superposition,[status(thm)],[c_32119,c_12335]) ).
tcf(c_62817,plain,
sK15(relation_inverse(sK1),sK15(sK1,apply(sK1,sK5(sK1,empty_set)))) = apply(sK1,sK15(sK1,apply(sK1,sK5(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_33222,c_12335]) ).
tcf(c_62821,plain,
sK15(relation_inverse(sK1),sK15(sK1,apply(sK1,sK22(sK1,empty_set)))) = apply(sK1,sK15(sK1,apply(sK1,sK22(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_40787,c_12335]) ).
tcf(c_62822,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK6(sK1,empty_set))) = sK6(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_62773,c_32127]) ).
tcf(c_62825,plain,
( empty(relation_dom(sK2))
| ( sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(light_normalisation,[status(thm)],[c_62727,c_34151]) ).
tcf(c_62826,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_62825,c_31365]) ).
tcf(c_62829,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK20(sK19(relation_dom(sK2))))) = apply(sK1,sK15(sK1,sK20(sK19(relation_dom(sK2))))),
inference(forward_subsumption_resolution,[status(thm)],[c_62820,c_31365]) ).
tcf(c_63443,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_12599]) ).
tcf(c_63449,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32125,c_12599]) ).
tcf(c_63457,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_12599]) ).
tcf(c_63458,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39302,c_12599]) ).
tcf(c_63459,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40624,c_12599]) ).
tcf(c_63460,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),apply(sK1,sK5(sK1,empty_set))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33228,c_12599]) ).
tcf(c_63461,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39676,c_12599]) ).
tcf(c_63463,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40100,c_12599]) ).
tcf(c_63465,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),apply(sK1,sK22(sK1,empty_set))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40793,c_12599]) ).
tcf(c_63492,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_63457,c_34151]) ).
tcf(c_63729,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set)))) = sK7(sK1,sK5(sK1,empty_set)),
inference(superposition,[status(thm)],[c_32739,c_12765]) ).
tcf(c_63733,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set)))) = sK7(sK1,sK22(sK1,empty_set)),
inference(superposition,[status(thm)],[c_40653,c_12765]) ).
tcf(c_63760,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_12765]) ).
tcf(c_63761,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,empty_set))))) = sK7(sK1,sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_12765]) ).
tcf(c_63762,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_12765]) ).
tcf(c_63763,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK24(empty_set,sK1))))) = sK7(sK1,sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_12765]) ).
tcf(c_63764,plain,
apply(sK1,sK22(sK1,empty_set)) = sK7(sK1,sK22(sK1,empty_set)),
inference(light_normalisation,[status(thm)],[c_63733,c_40661]) ).
tcf(c_63765,plain,
apply(sK1,sK5(sK1,empty_set)) = sK7(sK1,sK5(sK1,empty_set)),
inference(light_normalisation,[status(thm)],[c_63729,c_32746]) ).
tcf(c_63766,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_63686,c_31958]) ).
tcf(c_63767,plain,
apply(sK1,sK20(relation_dom(sK1))) = sK7(sK1,sK20(relation_dom(sK1))),
inference(forward_subsumption_resolution,[status(thm)],[c_63766,c_31369]) ).
tcf(c_63768,plain,
sK7(sK1,sK15(sK1,sK24(empty_set,sK1))) = sK24(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_63763,c_40627,c_40768]) ).
tcf(c_63769,plain,
sK7(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_63762,c_40105,c_40613]) ).
tcf(c_63770,plain,
sK7(sK1,sK15(sK1,sK21(sK1,empty_set))) = sK21(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_63761,c_39713,c_39942]) ).
tcf(c_63771,plain,
sK7(sK1,sK15(sK1,sK24(sK1,empty_set))) = sK24(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_63760,c_39305,c_39520]) ).
tcf(c_63772,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_63732,c_41530]) ).
tcf(c_63775,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_63731,c_41403]) ).
tcf(c_63778,plain,
( ( sK1 = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) ) ),
inference(light_normalisation,[status(thm)],[c_63730,c_40987]) ).
tcf(c_63781,plain,
( empty(relation_dom(sK1))
| ( apply(sK1,sK20(sK19(relation_dom(sK1)))) = sK7(sK1,sK20(sK19(relation_dom(sK1)))) ) ),
inference(light_normalisation,[status(thm)],[c_63759,c_36543]) ).
tcf(c_63782,plain,
apply(sK1,sK20(sK19(relation_dom(sK1)))) = sK7(sK1,sK20(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_63781,c_31369]) ).
tcf(c_63793,plain,
( ( relation_dom(sK1) = empty_set )
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_63714,c_61669]) ).
tcf(c_64177,plain,
( ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = sK7(sK1,sK13(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_61669,c_63810]) ).
tcf(c_64178,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK23(sK1,empty_set)) = sK7(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_40987,c_63810]) ).
tcf(c_64179,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK23(empty_set,sK1)) = sK7(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_41403,c_63810]) ).
tcf(c_64180,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK7(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_41530,c_63810]) ).
tcf(c_64181,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(relation_inverse(sK1),sK7(sK1,X0)),sK7(sK1,X0),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_63810,c_49]) ).
tcf(c_64182,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0)))) = apply(relation_inverse(sK1),sK7(sK1,X0)) )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),apply(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_63810,c_53]) ).
tcf(c_64183,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),apply(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_63810,c_52]) ).
tcf(c_64191,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_63810,c_54665]) ).
tcf(c_64192,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),apply(relation_inverse(sK1),sK7(sK1,X0))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_63810,c_54505]) ).
tcf(c_64193,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,X0)) = apply(sK2,sK7(sK1,X0)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_63810,c_53757]) ).
tcf(c_64256,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK7(sK1,X0))),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),apply(relation_inverse(sK1),sK7(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_64183,c_4013]) ).
tcf(c_64516,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61669,c_64231]) ).
tcf(c_64517,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40987,c_64231]) ).
tcf(c_64518,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41403,c_64231]) ).
tcf(c_64519,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41530,c_64231]) ).
tcf(c_64543,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK7(sK1,sK21(empty_set,sK1))),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64519,c_41530]) ).
tcf(c_64547,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK7(sK1,sK23(empty_set,sK1))),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64518,c_41403]) ).
tcf(c_64551,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK7(sK1,sK23(sK1,empty_set))),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64517,c_40987]) ).
tcf(c_64555,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),sK7(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_64516,c_61669]) ).
tcf(c_64593,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13385,c_49]) ).
tcf(c_64594,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))))) = sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_13385,c_53]) ).
tcf(c_64595,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_13385,c_52]) ).
tcf(c_64602,plain,
( in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13385,c_54665]) ).
tcf(c_64603,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_13385,c_54505]) ).
tcf(c_64604,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))) = apply(sK2,sK13(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_13385,c_53757]) ).
tcf(c_64656,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK13(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_64595,c_4013]) ).
tcf(c_65067,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(sK1,empty_set))))) = apply(sK1,sK15(sK1,sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39513,c_12766]) ).
tcf(c_65068,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,empty_set))))) = apply(sK1,sK15(sK1,sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39897,c_12766]) ).
tcf(c_65069,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(empty_set,sK1))))) = apply(sK1,sK15(sK1,sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40406,c_12766]) ).
tcf(c_65070,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK24(empty_set,sK1))))) = apply(sK1,sK15(sK1,sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40761,c_12766]) ).
tcf(c_65539,plain,
( element(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32001,c_13472]) ).
tcf(c_65540,plain,
( element(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32039,c_13472]) ).
tcf(c_65566,plain,
( element(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59821,c_13472]) ).
tcf(c_65567,plain,
( element(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61669,c_13472]) ).
tcf(c_65568,plain,
( element(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40931,c_13472]) ).
tcf(c_65569,plain,
( element(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40987,c_13472]) ).
tcf(c_65570,plain,
( element(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41214,c_13472]) ).
tcf(c_65571,plain,
( element(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41403,c_13472]) ).
tcf(c_65572,plain,
( element(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41474,c_13472]) ).
tcf(c_65573,plain,
( element(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41530,c_13472]) ).
tcf(c_65900,plain,
! [X0: $i] :
( in(X0,relation_dom(sK2))
| ( apply(sK2,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65899,c_31365]) ).
tcf(c_65921,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK2,sK20(relation_dom(sK2))) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32001,c_13473]) ).
tcf(c_65922,plain,
( in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32039,c_13473]) ).
tcf(c_65948,plain,
( in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59821,c_13473]) ).
tcf(c_65949,plain,
( in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_61669,c_13473]) ).
tcf(c_65950,plain,
( in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40931,c_13473]) ).
tcf(c_65951,plain,
( in(sK7(sK1,sK23(sK1,empty_set)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40987,c_13473]) ).
tcf(c_65952,plain,
( in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41214,c_13473]) ).
tcf(c_65953,plain,
( in(sK7(sK1,sK23(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41403,c_13473]) ).
tcf(c_65954,plain,
( in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41474,c_13473]) ).
tcf(c_65955,plain,
( in(sK7(sK1,sK21(empty_set,sK1)),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_41530,c_13473]) ).
tcf(c_66084,plain,
! [X0: $i] :
( sP0(X0,sK13(empty_set,relation_dom(sK2)),sK15(sK1,sK13(empty_set,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13387,c_49]) ).
tcf(c_66085,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13387,c_53]) ).
tcf(c_66086,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13387,c_52]) ).
tcf(c_66136,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66086,c_3821,c_4030]) ).
tcf(c_66141,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK13(empty_set,relation_dom(sK2)))) = sK13(empty_set,relation_dom(sK2)) )
| ~ in(sK13(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK13(empty_set,relation_dom(sK2))),sK13(empty_set,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66085,c_4030]) ).
tcf(c_66354,plain,
! [X0: $i] :
( sP0(X0,sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13933,c_49]) ).
tcf(c_66355,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13933,c_53]) ).
tcf(c_66356,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13933,c_52]) ).
tcf(c_66446,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66356,c_3821,c_4030]) ).
tcf(c_66459,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK5(sK1,relation_dom(sK2))) = sK6(sK1,relation_dom(sK2)) )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66355,c_4030]) ).
tcf(c_66816,plain,
! [X0: $i] :
( sP0(X0,sK5(sK1,relation_dom(sK2)),sK15(sK1,sK5(sK1,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_13935,c_49]) ).
tcf(c_66817,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13935,c_53]) ).
tcf(c_66818,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_13935,c_52]) ).
tcf(c_66908,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66818,c_3821,c_4030]) ).
tcf(c_66921,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(sK2,sK6(sK1,relation_dom(sK2))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2)))) = sK5(sK1,relation_dom(sK2)) )
| ~ in(sK5(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(sK1,relation_dom(sK2))),sK5(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_66817,c_4030]) ).
tcf(c_67249,plain,
sK15(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1))) = apply(sK1,sK5(empty_set,relation_dom(sK1))),
inference(global_subsumption_just,[status(thm)],[c_14024,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_14024,c_16946,c_19508,c_30801]) ).
tcf(c_67251,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_rng(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_67249,c_107]) ).
tcf(c_67252,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_67249,c_4472]) ).
tcf(c_67255,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_67251,c_3821]) ).
tcf(c_67256,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67255,c_3611]) ).
tcf(c_68397,plain,
apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_14027,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_14027,c_16946,c_19508,c_30801]) ).
tcf(c_68402,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1)),relation_inverse(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_68397,c_49]) ).
tcf(c_68403,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1))))) = apply(sK1,sK5(empty_set,relation_dom(sK1))) )
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_68397,c_53]) ).
tcf(c_68404,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_68397,c_52]) ).
tcf(c_68405,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_68397,c_87]) ).
tcf(c_68406,plain,
( in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_68397,c_13473]) ).
tcf(c_68407,plain,
( element(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_68397,c_13472]) ).
tcf(c_68408,plain,
( ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_68397,c_34564]) ).
tcf(c_68409,plain,
( element(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_68397,c_34565]) ).
tcf(c_68410,plain,
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_68397,c_34571]) ).
tcf(c_68411,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_68397,c_34529]) ).
tcf(c_68412,plain,
( ( sK15(sK1,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_68397,c_9713]) ).
tcf(c_68413,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_68397,c_13488]) ).
tcf(c_68414,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_68397,c_4623]) ).
tcf(c_68415,plain,
( ( sK15(sK1,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_68397,c_4763]) ).
tcf(c_68416,plain,
( ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ( sK15(sK1,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_68397,c_56725]) ).
tcf(c_68417,plain,
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( sK5(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_68410,c_68397]) ).
tcf(c_68428,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( sK5(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_68411,c_68397]) ).
tcf(c_68431,plain,
( element(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( sK5(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_68409,c_68397]) ).
tcf(c_68434,plain,
( ( sK5(empty_set,relation_dom(sK1)) = empty_set )
| ( sK15(sK1,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_68412,c_68397]) ).
tcf(c_68437,plain,
( ( sK5(empty_set,relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_68408,c_68397]) ).
tcf(c_68446,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_68405,c_4030]) ).
tcf(c_68447,plain,
( in(ordered_pair(apply(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68446,c_987,c_3611]) ).
tcf(c_68450,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_68413,c_68397]) ).
tcf(c_68454,plain,
! [X0: $i] :
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_68404,c_3821,c_4030,c_68397]) ).
tcf(c_68458,plain,
! [X0: $i] :
( ( apply(X0,sK5(empty_set,relation_dom(sK1))) = apply(sK1,sK5(empty_set,relation_dom(sK1))) )
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_68403,c_4030,c_68397]) ).
tcf(c_68988,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = relation_dom(sK12) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_dom(sK12)))) = sK5(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68503,c_4997]) ).
tcf(c_69269,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = relation_dom(sK12) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_dom(sK12)))) = sK14(sK1,relation_dom(sK12)) )
| ~ empty(relation_rng(sK12)) ),
inference(superposition,[status(thm)],[c_68508,c_4997]) ).
tcf(c_69366,plain,
apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)),
inference(global_subsumption_just,[status(thm)],[c_14028,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_14028,c_16946,c_19508,c_30801]) ).
tcf(c_69372,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1)),relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_69366,c_49]) ).
tcf(c_69373,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1))))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_69366,c_53]) ).
tcf(c_69374,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),relation_rng(relation_inverse(sK1)))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_69366,c_52]) ).
tcf(c_69375,plain,
( in(ordered_pair(sK7(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(relation_inverse(sK1))) ),
inference(superposition,[status(thm)],[c_69366,c_87]) ).
tcf(c_69376,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_69366,c_64231]) ).
tcf(c_69377,plain,
( ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(superposition,[status(thm)],[c_69366,c_63810]) ).
tcf(c_69378,plain,
( ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ( sK15(sK1,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(superposition,[status(thm)],[c_69366,c_55855]) ).
tcf(c_69379,plain,
( in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_69366,c_13473]) ).
tcf(c_69380,plain,
( element(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_69366,c_13472]) ).
tcf(c_69381,plain,
( ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK1,ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))))) ),
inference(superposition,[status(thm)],[c_69366,c_34564]) ).
tcf(c_69382,plain,
( element(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_34565]) ).
tcf(c_69383,plain,
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_34571]) ).
tcf(c_69384,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_34529]) ).
tcf(c_69385,plain,
( ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_12764]) ).
tcf(c_69386,plain,
( ( sK15(sK1,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_9713]) ).
tcf(c_69387,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_69366,c_13488]) ).
tcf(c_69388,plain,
( ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) )
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_12807]) ).
tcf(c_69389,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69366,c_4623]) ).
tcf(c_69390,plain,
( ( sK15(sK1,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_69366,c_4763]) ).
tcf(c_69404,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( sK5(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_69384,c_69366]) ).
tcf(c_69407,plain,
( element(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( sK5(empty_set,relation_dom(sK1)) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_69382,c_69366]) ).
tcf(c_69410,plain,
( ( sK5(empty_set,relation_dom(sK1)) = empty_set )
| ( sK15(sK1,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = sK5(empty_set,relation_dom(sK1)) ) ),
inference(light_normalisation,[status(thm)],[c_69386,c_69366]) ).
tcf(c_69413,plain,
( ( sK5(empty_set,relation_dom(sK1)) = empty_set )
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) ) ),
inference(light_normalisation,[status(thm)],[c_69385,c_69366]) ).
tcf(c_69416,plain,
( ( sK5(empty_set,relation_dom(sK1)) = empty_set )
| ~ in(sK1,ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))))) ),
inference(light_normalisation,[status(thm)],[c_69381,c_69366]) ).
tcf(c_69425,plain,
( in(ordered_pair(sK7(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ function(relation_inverse(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_69375,c_4030]) ).
tcf(c_69426,plain,
( in(ordered_pair(sK7(sK1,sK5(empty_set,relation_dom(sK1))),sK5(empty_set,relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69425,c_987,c_3611]) ).
tcf(c_69429,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_69376,c_69366]) ).
tcf(c_69433,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_69387,c_69366]) ).
tcf(c_69437,plain,
! [X0: $i] :
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_69374,c_3821,c_4030,c_69366]) ).
tcf(c_69441,plain,
! [X0: $i] :
( ( apply(X0,sK5(empty_set,relation_dom(sK1))) = sK7(sK1,sK5(empty_set,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(empty_set,relation_dom(sK1)),sK7(sK1,sK5(empty_set,relation_dom(sK1))),X0) ),
inference(light_normalisation,[status(thm)],[c_69373,c_4030,c_69366]) ).
tcf(c_69994,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK2,apply(sK1,sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69489,c_4997]) ).
tcf(c_70547,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,apply(sK1,sK14(sK1,relation_rng(sK12)))) = sK14(sK1,relation_rng(sK12)) )
| ~ empty(relation_dom(sK12)) ),
inference(superposition,[status(thm)],[c_69495,c_4997]) ).
tcf(c_70650,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_14030,c_49]) ).
tcf(c_70651,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))) = apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_14030,c_53]) ).
tcf(c_70652,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_14030,c_52]) ).
tcf(c_70660,plain,
( in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14030,c_54665]) ).
tcf(c_70661,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14030,c_54505]) ).
tcf(c_70662,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = apply(sK2,sK5(empty_set,relation_dom(sK2))) )
| ( apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14030,c_53757]) ).
tcf(c_70705,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_70652,c_4013]) ).
tcf(c_70789,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),sK1)
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_14032,c_49]) ).
tcf(c_70790,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))))) = sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_14032,c_53]) ).
tcf(c_70791,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_rng(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(superposition,[status(thm)],[c_14032,c_52]) ).
tcf(c_70798,plain,
( in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14032,c_54665]) ).
tcf(c_70799,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_14032,c_54505]) ).
tcf(c_70800,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = empty_set )
| ( sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))) = apply(sK2,sK5(empty_set,relation_dom(sK2))) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_14032,c_53757]) ).
tcf(c_70852,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))),relation_dom(sK2))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ~ sP0(sK1,sK5(empty_set,relation_dom(sK2)),sK7(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),X0) ),
inference(light_normalisation,[status(thm)],[c_70791,c_4013]) ).
tcf(c_70882,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(relation_inverse(sK1),relation_rng(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_9702]) ).
tcf(c_70906,plain,
! [X0: $i] :
( sP0(X0,relation_dom(sK2),empty_set,relation_inverse(sK1))
| ~ in(relation_dom(sK2),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_70881,c_49]) ).
tcf(c_70907,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_70881,c_53]) ).
tcf(c_70908,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),relation_dom(sK2)),relation_rng(relation_inverse(sK1)))
| ~ in(relation_dom(sK2),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_70881,c_52]) ).
tcf(c_70944,plain,
! [X0: $i] :
( in(empty_set,relation_dom(sK1))
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,relation_dom(sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_70908,c_3821,c_4030,c_70881]) ).
tcf(c_70948,plain,
! [X0: $i] :
( ( apply(X0,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,relation_dom(sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_70907,c_4030,c_70881]) ).
tcf(c_71032,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_71015,c_4997]) ).
tcf(c_71068,plain,
! [X0: $i] :
( sP0(X0,relation_dom(sK2),empty_set,sK2)
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_70919,c_49]) ).
tcf(c_71069,plain,
! [X0: $i] :
( ( apply(sK1,empty_set) = relation_dom(sK2) )
| ( apply(X0,apply(sK2,relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_70919,c_53]) ).
tcf(c_71070,plain,
! [X0: $i] :
( in(apply(sK2,relation_dom(sK2)),relation_rng(sK2))
| ( apply(sK1,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_70919,c_52]) ).
tcf(c_71145,plain,
! [X0: $i] :
( sP0(X0,sK5(empty_set,relation_dom(sK2)),sK15(sK1,sK5(empty_set,relation_dom(sK2))),relation_inverse(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_14034,c_49]) ).
tcf(c_71146,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_14034,c_53]) ).
tcf(c_71147,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_14034,c_52]) ).
tcf(c_71197,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK2) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_71147,c_3821,c_4030]) ).
tcf(c_71202,plain,
! [X0: $i] :
( ( relation_dom(sK2) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK5(empty_set,relation_dom(sK2)))) = sK5(empty_set,relation_dom(sK2)) )
| ~ in(sK5(empty_set,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK5(empty_set,relation_dom(sK2))),sK5(empty_set,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_71146,c_4030]) ).
tcf(c_71307,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,empty_set),empty_set,relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_71034,c_49]) ).
tcf(c_71308,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,empty_set))) = apply(sK1,empty_set) )
| ~ in(apply(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,apply(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_71034,c_53]) ).
tcf(c_71309,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,apply(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_71034,c_52]) ).
tcf(c_71354,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,empty_set)),relation_dom(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(apply(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,apply(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_71309,c_3821,c_4030]) ).
tcf(c_71359,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),apply(sK1,empty_set))) = apply(sK1,empty_set) )
| ~ in(apply(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,apply(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_71308,c_4030]) ).
tcf(c_71581,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,empty_set),empty_set,relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK7(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_71035,c_49]) ).
tcf(c_71582,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,empty_set))) = sK7(sK1,empty_set) )
| ~ in(sK7(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK7(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_71035,c_53]) ).
tcf(c_71583,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK7(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK7(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_71035,c_52]) ).
tcf(c_71642,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK7(sK1,empty_set)),relation_dom(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(sK7(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK7(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_71583,c_3821,c_4030]) ).
tcf(c_71647,plain,
! [X0: $i] :
( ( apply(sK2,relation_dom(sK2)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK7(sK1,empty_set))) = sK7(sK1,empty_set) )
| ~ in(sK7(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK7(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_71582,c_4030]) ).
tcf(c_71779,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK15(sK1,sK7(sK1,X0)),sK7(sK1,X0),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_64168,c_49]) ).
tcf(c_71780,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK1,sK15(sK1,sK7(sK1,X0)))) = sK15(sK1,sK7(sK1,X0)) )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK15(sK1,sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_64168,c_53]) ).
tcf(c_71781,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK15(sK1,sK7(sK1,X0))),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK15(sK1,sK7(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_64168,c_52]) ).
tcf(c_71788,plain,
! [X0: $i] :
( in(sK15(sK1,sK7(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(sK7(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64168,c_54665]) ).
tcf(c_71789,plain,
! [X0: $i] :
( in(ordered_pair(sK7(sK1,X0),sK15(sK1,sK7(sK1,X0))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK7(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64168,c_54505]) ).
tcf(c_71790,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = sK15(sK1,sK7(sK1,X0)) )
| ( apply(sK1,sK15(sK1,sK7(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_64168,c_53757]) ).
tcf(c_71834,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,sK15(sK1,sK7(sK1,X0))),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,sK7(sK1,X0),sK15(sK1,sK7(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_71781,c_4013]) ).
tcf(c_72351,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK13(sK1,relation_dom(sK1))),empty_set,sK2)
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_15829,c_49]) ).
tcf(c_72352,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(X0,apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1))))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_15829,c_53]) ).
tcf(c_72353,plain,
! [X0: $i] :
( in(apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))),relation_rng(sK2))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_dom(sK1))) = sK7(sK1,sK13(sK1,relation_dom(sK1))) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK13(sK1,relation_dom(sK1))),X0) ),
inference(superposition,[status(thm)],[c_15829,c_52]) ).
tcf(c_72584,plain,
! [X0: $i,X1: $i] :
( sP0(X1,sK7(sK1,X0),X0,relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,sK7(sK1,X0)) = empty_set )
| ~ in(sK7(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_56204,c_4838]) ).
tcf(c_72585,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(sK1,X0),X0,relation_inverse(sK1))
| ( apply(sK1,X0) = empty_set )
| ( apply(sK2,apply(sK1,X0)) = empty_set )
| ~ in(apply(sK1,X0),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_57193,c_4838]) ).
tcf(c_72586,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1)),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(apply(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_14967,c_4838]) ).
tcf(c_72587,plain,
! [X0: $i] :
( sP0(X0,relation_dom(sK2),empty_set,relation_inverse(sK1))
| ( apply(sK2,relation_dom(sK2)) = empty_set )
| ~ in(relation_dom(sK2),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_70921,c_4838]) ).
tcf(c_73218,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK13(sK1,relation_dom(sK1))),sK13(sK1,relation_dom(sK1)),relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_dom(sK1))) = sK14(sK1,relation_dom(sK1)) )
| ( apply(sK2,sK7(sK1,sK13(sK1,relation_dom(sK1)))) = empty_set )
| ~ in(sK7(sK1,sK13(sK1,relation_dom(sK1))),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_15831,c_4838]) ).
tcf(c_73299,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,relation_rng(sK12)) = empty_set )
| ( apply(relation_inverse(sK12),relation_rng(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_rng(sK12))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_31455]) ).
tcf(c_73343,plain,
( empty(sK20(powerset(relation_dom(sK1))))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(sK20(powerset(relation_dom(sK1)))))) = sK20(sK20(powerset(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_73325,c_4997]) ).
tcf(c_73451,plain,
! [X0: $i] :
( sP0(X0,relation_rng(sK12),empty_set,relation_inverse(sK12))
| ~ in(relation_rng(sK12),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_73300,c_49]) ).
tcf(c_73452,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK12),relation_rng(sK12))) = relation_rng(sK12) )
| ~ in(relation_rng(sK12),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,relation_rng(sK12),X0) ),
inference(superposition,[status(thm)],[c_73300,c_53]) ).
tcf(c_73453,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK12),relation_rng(sK12)),relation_rng(relation_inverse(sK12)))
| ~ in(relation_rng(sK12),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,relation_rng(sK12),X0) ),
inference(superposition,[status(thm)],[c_73300,c_52]) ).
tcf(c_73461,plain,
! [X0: $i] :
( in(empty_set,relation_dom(sK12))
| ~ in(relation_rng(sK12),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,relation_rng(sK12),X0) ),
inference(light_normalisation,[status(thm)],[c_73453,c_3810,c_3820,c_73300]) ).
tcf(c_73465,plain,
! [X0: $i] :
( ( apply(X0,empty_set) = relation_rng(sK12) )
| ~ in(relation_rng(sK12),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,relation_rng(sK12),X0) ),
inference(light_normalisation,[status(thm)],[c_73452,c_3810,c_73300]) ).
tcf(c_81647,plain,
! [X0: $i] :
( sP0(X0,sK22(sK1,sK1),sK21(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_17971,c_49]) ).
tcf(c_81648,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_17971,c_53]) ).
tcf(c_81649,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_17971,c_52]) ).
tcf(c_81730,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_81649,c_3821,c_4030]) ).
tcf(c_81741,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(sK1,sK1),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_81648,c_4030]) ).
tcf(c_85474,plain,
! [X0: $i] :
( in(sK23(sK1,X0),relation_dom(X0))
| ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,X0))) = sK23(sK1,X0) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8860,c_4997]) ).
tcf(c_85824,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK1,sK2)) = sK15(sK1,sK23(sK1,sK2)) )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85549,c_4997]) ).
tcf(c_85881,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85553,c_4997]) ).
tcf(c_85931,plain,
! [X0: $i] :
( sP0(X0,sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18305,c_49]) ).
tcf(c_85932,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_18305,c_53]) ).
tcf(c_85933,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_18305,c_52]) ).
tcf(c_86023,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_85933,c_3821,c_4030]) ).
tcf(c_86036,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(sK1,sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_85932,c_4030]) ).
tcf(c_86361,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85557,c_4997]) ).
tcf(c_86552,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(sK1,apply(sK2,sK23(sK1,sK2))) = sK23(sK1,sK2) ) ),
inference(superposition,[status(thm)],[c_85574,c_4997]) ).
tcf(c_86620,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85579,c_4997]) ).
tcf(c_86677,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK1,sK2)))) = sK15(sK1,sK23(sK1,sK2)) ) ),
inference(superposition,[status(thm)],[c_85583,c_4997]) ).
tcf(c_86734,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,sK2))) = sK23(sK1,sK2) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK1,sK2))) = apply(sK1,sK15(sK1,sK23(sK1,sK2))) ) ),
inference(superposition,[status(thm)],[c_85587,c_4997]) ).
tcf(c_86863,plain,
! [X0: $i] :
( in(sK23(X0,sK1),relation_dom(X0))
| ( X0 = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(X0,sK1))) = sK23(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_8979,c_4997]) ).
tcf(c_87025,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK23(sK2,sK1)) = sK15(sK1,sK23(sK2,sK1)) )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86938,c_4997]) ).
tcf(c_87131,plain,
! [X0: $i] :
( sP0(X0,sK22(sK1,sK1),sK15(sK1,sK22(sK1,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_18307,c_49]) ).
tcf(c_87132,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_18307,c_53]) ).
tcf(c_87133,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(superposition,[status(thm)],[c_18307,c_52]) ).
tcf(c_87222,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK1,sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_87133,c_3821,c_4030]) ).
tcf(c_87235,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( sK15(sK1,sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK21(sK1,sK1)) = empty_set )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(sK22(sK1,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_87132,c_4030]) ).
tcf(c_88535,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86942,c_4997]) ).
tcf(c_88592,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86946,c_4997]) ).
tcf(c_88870,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(sK1,apply(sK2,sK23(sK2,sK1))) = sK23(sK2,sK1) ) ),
inference(superposition,[status(thm)],[c_86963,c_4997]) ).
tcf(c_88938,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86968,c_4997]) ).
tcf(c_88995,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK23(sK2,sK1)))) = sK15(sK1,sK23(sK2,sK1)) ) ),
inference(superposition,[status(thm)],[c_86972,c_4997]) ).
tcf(c_89052,plain,
( ( sK1 = sK2 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK2,sK1))) = sK23(sK2,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK23(sK2,sK1))) = apply(sK1,sK15(sK1,sK23(sK2,sK1))) ) ),
inference(superposition,[status(thm)],[c_86976,c_4997]) ).
tcf(c_89129,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK7(relation_inverse(sK1),relation_rng(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_89104]) ).
tcf(c_89161,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_20404,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_16946,c_19508,c_20404,c_30801]) ).
tcf(c_89162,plain,
( ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(renaming,[status(thm)],[c_89161]) ).
tcf(c_89167,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,empty_set),empty_set,sK2)
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_89162,c_49]) ).
tcf(c_89168,plain,
! [X0: $i] :
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ( apply(X0,apply(sK2,sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89162,c_53]) ).
tcf(c_89169,plain,
! [X0: $i] :
( in(apply(sK2,sK6(sK1,empty_set)),relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89162,c_52]) ).
tcf(c_89172,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89162,c_19430]) ).
tcf(c_89173,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89162,c_4045]) ).
tcf(c_89174,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89162,c_19431]) ).
tcf(c_89175,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89162,c_18734]) ).
tcf(c_89176,plain,
( in(ordered_pair(sK6(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89162,c_87]) ).
tcf(c_89180,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89175,c_32119]) ).
tcf(c_89184,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89174,c_32119]) ).
tcf(c_89188,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89173,c_32119]) ).
tcf(c_89192,plain,
( in(ordered_pair(sK6(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89176,c_62,c_61,c_32119]) ).
tcf(c_89195,plain,
! [X0: $i] :
( in(apply(sK2,sK6(sK1,empty_set)),relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ sP0(sK2,empty_set,sK6(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89169,c_32119]) ).
tcf(c_89199,plain,
! [X0: $i] :
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ( apply(X0,apply(sK2,sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ sP0(sK2,empty_set,sK6(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89168,c_32119]) ).
tcf(c_89238,plain,
~ in(sK1,ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_33209,c_70]) ).
tcf(c_89239,plain,
element(ordered_pair(sK5(sK1,empty_set),apply(sK1,sK5(sK1,empty_set))),sK1),
inference(superposition,[status(thm)],[c_33209,c_69]) ).
tcf(c_89241,plain,
( ( relation_dom(sK1) = empty_set )
| ~ relation(sK1)
| ~ in(sK5(sK1,empty_set),empty_set) ),
inference(superposition,[status(thm)],[c_33209,c_76]) ).
tcf(c_89242,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_33209,c_106]) ).
tcf(c_89248,plain,
( in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_89242,c_4013]) ).
tcf(c_89284,plain,
( empty(relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))) ) ),
inference(superposition,[status(thm)],[c_89256,c_4997]) ).
tcf(c_89318,plain,
apply(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89296,c_31365]) ).
tcf(c_89319,plain,
apply(sK1,sK7(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_89295,c_31365]) ).
tcf(c_89320,plain,
apply(sK1,apply(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))),
inference(forward_subsumption_resolution,[status(thm)],[c_89294,c_31365]) ).
tcf(c_89321,plain,
apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_89287,c_31369]) ).
tcf(c_89322,plain,
apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_89286,c_31369]) ).
tcf(c_89323,plain,
sK15(relation_inverse(sK1),sK20(sK19(sK19(relation_dom(sK1))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89285,c_31369]) ).
tcf(c_89324,plain,
( ( apply(sK2,sK7(relation_inverse(sK2),sK20(sK19(sK19(relation_rng(sK2)))))) = sK20(sK19(sK19(relation_rng(sK2)))) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89300,c_31370]) ).
tcf(c_89327,plain,
( ( sK15(relation_inverse(sK2),sK20(sK19(sK19(relation_dom(sK2))))) = apply(sK2,sK20(sK19(sK19(relation_dom(sK2))))) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89293,c_31365]) ).
tcf(c_89330,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(sK19(sK19(relation_dom(sK2)))))) = sK20(sK19(sK19(relation_dom(sK2)))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89292,c_31365]) ).
tcf(c_89333,plain,
apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89291,c_31365]) ).
tcf(c_89334,plain,
apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))))) = sK15(sK1,sK20(sK19(sK19(relation_dom(sK2))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89290,c_31365]) ).
tcf(c_89335,plain,
sK15(relation_inverse(sK1),sK15(sK1,sK20(sK19(sK19(relation_dom(sK2)))))) = apply(sK1,sK15(sK1,sK20(sK19(sK19(relation_dom(sK2)))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89289,c_31365]) ).
tcf(c_89336,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK20(sK19(sK19(relation_dom(sK1)))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89284,c_31369]) ).
tcf(c_89339,plain,
apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK15(sK1,sK7(sK1,sK20(sK19(sK19(relation_dom(sK1)))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89283,c_31369]) ).
tcf(c_89340,plain,
apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))) = sK15(sK1,apply(sK1,sK20(sK19(sK19(relation_dom(sK1)))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89282,c_31369]) ).
tcf(c_89341,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89281,c_31369]) ).
tcf(c_89342,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89280,c_31369]) ).
tcf(c_89343,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = sK7(sK1,sK20(sK19(sK19(relation_dom(sK1))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89279,c_31369]) ).
tcf(c_89344,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))))) = apply(sK1,sK20(sK19(sK19(relation_dom(sK1))))),
inference(forward_subsumption_resolution,[status(thm)],[c_89278,c_31369]) ).
tcf(c_89439,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(sK2,ordered_pair(sK6(sK1,empty_set),empty_set)) ),
inference(superposition,[status(thm)],[c_89192,c_70]) ).
tcf(c_89440,plain,
( element(ordered_pair(sK6(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_89192,c_69]) ).
tcf(c_89442,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_89192,c_106]) ).
tcf(c_89447,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89442,c_61]) ).
tcf(c_89459,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(relation_rng(sK2),empty_set) ),
inference(superposition,[status(thm)],[c_89447,c_70]) ).
tcf(c_89460,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_89447,c_69]) ).
tcf(c_89462,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ( apply(sK2,sK7(relation_inverse(sK2),empty_set)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_89447,c_43161]) ).
tcf(c_89498,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK2) = X0 )
| ( apply(sK2,sK13(sK1,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK14(sK1,X0))) = sK14(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_10592,c_4997]) ).
tcf(c_89644,plain,
sK15(sK1,sK6(sK1,empty_set)) = sK5(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_20406,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_16946,c_19508,c_30801,c_32081]) ).
tcf(c_89646,plain,
apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK5(sK1,empty_set),
inference(demodulation,[status(thm)],[c_32079,c_89644]) ).
tcf(c_89647,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ~ relation(sK1)
| ~ in(sK6(sK1,empty_set),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_89644,c_107]) ).
tcf(c_89648,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1))
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89644,c_4848]) ).
tcf(c_89649,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,empty_set),sK5(sK1,empty_set),relation_inverse(sK1))
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_89644,c_4838]) ).
tcf(c_89652,plain,
( ( apply(sK2,sK6(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_89644,c_59117]) ).
tcf(c_89655,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_89644,c_34537]) ).
tcf(c_89664,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ~ relation(sK1)
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_89647,c_4013]) ).
tcf(c_89665,plain,
in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_89664,c_64,c_32119]) ).
tcf(c_89670,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1))
| ( apply(sK2,sK6(sK1,empty_set)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89648,c_32119]) ).
tcf(c_89686,plain,
~ in(sK1,ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set))),
inference(superposition,[status(thm)],[c_89665,c_70]) ).
tcf(c_89687,plain,
element(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1),
inference(superposition,[status(thm)],[c_89665,c_69]) ).
tcf(c_89690,plain,
( in(sK6(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89665,c_106]) ).
tcf(c_89692,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ function(sK1)
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_89665,c_197]) ).
tcf(c_89696,plain,
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_89690,c_4013]) ).
tcf(c_89697,plain,
apply(sK1,sK5(sK1,empty_set)) = sK6(sK1,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_89692,c_65,c_64]) ).
tcf(c_89700,plain,
element(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_33213,c_89697]) ).
tcf(c_89707,plain,
in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_33211,c_89697]) ).
tcf(c_89708,plain,
sK15(relation_inverse(sK1),sK5(sK1,empty_set)) = sK6(sK1,empty_set),
inference(demodulation,[status(thm)],[c_32744,c_89697]) ).
tcf(c_89710,plain,
! [X0: $i] :
( sP0(X0,sK5(sK1,empty_set),sK6(sK1,empty_set),sK1)
| ~ in(sK5(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_89697,c_49]) ).
tcf(c_89711,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK5(sK1,empty_set))) = sK5(sK1,empty_set) )
| ~ in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK5(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89697,c_53]) ).
tcf(c_89712,plain,
! [X0: $i] :
( in(apply(sK1,sK5(sK1,empty_set)),relation_rng(sK1))
| ~ in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK5(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89697,c_52]) ).
tcf(c_89715,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_89697,c_61586]) ).
tcf(c_89719,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK6(sK1,empty_set)) = sK15(sK1,sK6(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_89697,c_56725]) ).
tcf(c_89721,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK5(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_89697,c_54505]) ).
tcf(c_89722,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK6(sK1,empty_set)) = sK5(sK1,empty_set) )
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_89697,c_53757]) ).
tcf(c_89730,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ( apply(sK2,sK6(sK1,empty_set)) = sK5(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_89722,c_89697]) ).
tcf(c_89734,plain,
! [X0: $i] :
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK5(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_89712,c_4013,c_89697]) ).
tcf(c_89735,plain,
! [X0: $i] :
( ( apply(X0,sK6(sK1,empty_set)) = sK5(sK1,empty_set) )
| ~ in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK6(sK1,empty_set),sK5(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_89711,c_89697]) ).
tcf(c_89736,plain,
! [X0: $i] :
( ( apply(X0,sK6(sK1,empty_set)) = sK5(sK1,empty_set) )
| ~ sP0(sK1,sK6(sK1,empty_set),sK5(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89735,c_32739]) ).
tcf(c_89739,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_89721,c_89697]) ).
tcf(c_89740,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89739,c_32119]) ).
tcf(c_89748,plain,
~ in(relation_inverse(sK1),ordered_pair(sK6(sK1,empty_set),sK5(sK1,empty_set))),
inference(superposition,[status(thm)],[c_89707,c_70]) ).
tcf(c_89752,plain,
( in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_89707,c_78]) ).
tcf(c_89756,plain,
( in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_89752,c_4030]) ).
tcf(c_91818,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_12604]) ).
tcf(c_91824,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32125,c_12604]) ).
tcf(c_91836,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_12604]) ).
tcf(c_91837,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39302,c_12604]) ).
tcf(c_91838,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40624,c_12604]) ).
tcf(c_91840,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39676,c_12604]) ).
tcf(c_91842,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40100,c_12604]) ).
tcf(c_91844,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),relation_inverse(sK1))
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40793,c_12604]) ).
tcf(c_91867,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91836,c_34151]) ).
tcf(c_91893,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK7(relation_inverse(sK1),sK22(empty_set,sK1))),relation_inverse(sK1))
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91842,c_40100]) ).
tcf(c_91897,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK7(relation_inverse(sK1),sK21(sK1,empty_set))),relation_inverse(sK1))
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91840,c_39676]) ).
tcf(c_91901,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK7(relation_inverse(sK1),sK24(empty_set,sK1))),relation_inverse(sK1))
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91838,c_40624]) ).
tcf(c_91905,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK7(relation_inverse(sK1),sK24(sK1,empty_set))),relation_inverse(sK1))
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91837,c_39302]) ).
tcf(c_91909,plain,
( in(ordered_pair(sK6(sK1,empty_set),sK7(relation_inverse(sK1),sK6(sK1,empty_set))),relation_inverse(sK1))
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91824,c_32125]) ).
tcf(c_91913,plain,
( in(ordered_pair(sK20(relation_dom(sK2)),sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91818,c_33899]) ).
tcf(c_91950,plain,
( in(ordered_pair(apply(sK1,sK22(sK1,empty_set)),sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set)))),relation_inverse(sK1))
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_91844,c_40793]) ).
tcf(c_92027,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(sK1) = X0 )
| ( apply(sK1,sK5(sK1,X0)) = empty_set )
| ( apply(sK2,apply(sK1,sK5(sK1,X0))) = sK5(sK1,X0) ) ),
inference(superposition,[status(thm)],[c_12635,c_4997]) ).
tcf(c_92855,plain,
~ in(sK1,ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39482,c_70]) ).
tcf(c_92856,plain,
element(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1),
inference(superposition,[status(thm)],[c_39482,c_69]) ).
tcf(c_92858,plain,
( in(sK24(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_39482,c_106]) ).
tcf(c_92864,plain,
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_92858,c_4013]) ).
tcf(c_92882,plain,
( ( apply(sK2,apply(sK1,sK20(relation_dom(sK1)))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK20(relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_32039,c_13471]) ).
tcf(c_92911,plain,
( ( apply(sK2,apply(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK13(empty_set,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_59821,c_13471]) ).
tcf(c_92912,plain,
( ( apply(sK2,sK7(sK1,sK13(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK13(empty_set,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_61669,c_13471]) ).
tcf(c_92914,plain,
( ( apply(sK2,apply(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK5(empty_set,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_68397,c_13471]) ).
tcf(c_92915,plain,
( ( apply(sK2,sK7(sK1,sK5(empty_set,relation_dom(sK1)))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK5(empty_set,relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_69366,c_13471]) ).
tcf(c_92917,plain,
( ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK23(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_40931,c_13471]) ).
tcf(c_92918,plain,
( ( apply(sK2,sK7(sK1,sK23(sK1,empty_set))) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK23(sK1,empty_set))) ),
inference(superposition,[status(thm)],[c_40987,c_13471]) ).
tcf(c_92919,plain,
( ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK23(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_41214,c_13471]) ).
tcf(c_92920,plain,
( ( apply(sK2,sK7(sK1,sK23(empty_set,sK1))) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK23(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_41403,c_13471]) ).
tcf(c_92921,plain,
( ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),apply(sK1,sK21(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_41474,c_13471]) ).
tcf(c_92922,plain,
( ( apply(sK2,sK7(sK1,sK21(empty_set,sK1))) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ in(relation_dom(sK2),sK7(sK1,sK21(empty_set,sK1))) ),
inference(superposition,[status(thm)],[c_41530,c_13471]) ).
tcf(c_93221,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),relation_rng(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_92951]) ).
tcf(c_93258,plain,
apply(sK1,sK23(sK1,empty_set)) = sK24(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_23301,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801,c_39023]) ).
tcf(c_93260,plain,
apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK23(sK1,empty_set),
inference(demodulation,[status(thm)],[c_40931,c_93258]) ).
tcf(c_93261,plain,
sK15(relation_inverse(sK1),sK23(sK1,empty_set)) = sK24(sK1,empty_set),
inference(demodulation,[status(thm)],[c_40921,c_93258]) ).
tcf(c_93262,plain,
sK15(sK1,sK24(sK1,empty_set)) = sK23(sK1,empty_set),
inference(demodulation,[status(thm)],[c_39303,c_93260]) ).
tcf(c_93263,plain,
in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1),
inference(demodulation,[status(thm)],[c_39482,c_93262]) ).
tcf(c_93265,plain,
element(sK23(sK1,empty_set),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_39515,c_93262]) ).
tcf(c_93266,plain,
in(sK23(sK1,empty_set),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_39513,c_93262]) ).
tcf(c_93267,plain,
in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_39492,c_93262]) ).
tcf(c_93268,plain,
! [X0: $i] :
( sP0(X0,sK23(sK1,empty_set),sK24(sK1,empty_set),sK1)
| ~ in(sK23(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_93258,c_49]) ).
tcf(c_93269,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK23(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_93258,c_53]) ).
tcf(c_93270,plain,
! [X0: $i] :
( in(apply(sK1,sK23(sK1,empty_set)),relation_rng(sK1))
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK23(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_93258,c_52]) ).
tcf(c_93274,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_93258,c_61586]) ).
tcf(c_93278,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(sK1,empty_set)) = sK15(sK1,sK24(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_93258,c_56725]) ).
tcf(c_93279,plain,
( in(sK23(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93258,c_54665]) ).
tcf(c_93280,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK23(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_93258,c_54505]) ).
tcf(c_93281,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(sK1,empty_set)) = sK23(sK1,empty_set) )
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_93258,c_53757]) ).
tcf(c_93289,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ( apply(sK2,sK24(sK1,empty_set)) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_93281,c_93258]) ).
tcf(c_93293,plain,
! [X0: $i] :
( in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK23(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_93270,c_4013,c_93258]) ).
tcf(c_93294,plain,
( in(sK23(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_93279,c_93258]) ).
tcf(c_93295,plain,
( in(sK23(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93294,c_39295]) ).
tcf(c_93299,plain,
! [X0: $i] :
( ( apply(X0,sK24(sK1,empty_set)) = sK23(sK1,empty_set) )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK24(sK1,empty_set),sK23(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_93269,c_93258]) ).
tcf(c_93303,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_93280,c_93258]) ).
tcf(c_93304,plain,
( in(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_93303,c_39295]) ).
tcf(c_93311,plain,
element(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1),
inference(light_normalisation,[status(thm)],[c_92856,c_93262]) ).
tcf(c_93756,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set)))) = apply(sK1,sK23(sK1,empty_set)),
inference(superposition,[status(thm)],[c_93266,c_12766]) ).
tcf(c_93757,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set)))) = sK7(sK1,sK23(sK1,empty_set)),
inference(superposition,[status(thm)],[c_93266,c_12765]) ).
tcf(c_93758,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set)))) = apply(sK1,sK23(sK1,empty_set)),
inference(superposition,[status(thm)],[c_93266,c_10203]) ).
tcf(c_93759,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set)))) = sK7(sK1,sK23(sK1,empty_set)),
inference(superposition,[status(thm)],[c_93266,c_10202]) ).
tcf(c_93760,plain,
apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = sK15(sK1,apply(sK1,sK23(sK1,empty_set))),
inference(superposition,[status(thm)],[c_93266,c_6249]) ).
tcf(c_93761,plain,
apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = sK15(sK1,sK7(sK1,sK23(sK1,empty_set))),
inference(superposition,[status(thm)],[c_93266,c_5349]) ).
tcf(c_93762,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_93266,c_4997]) ).
tcf(c_93766,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(sK1,empty_set)) = sK23(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_93762,c_93258]) ).
tcf(c_93769,plain,
sK15(sK1,sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_93761,c_40987]) ).
tcf(c_93772,plain,
sK7(sK1,sK23(sK1,empty_set)) = sK24(sK1,empty_set),
inference(light_normalisation,[status(thm)],[c_93757,c_40987,c_93258]) ).
tcf(c_93775,plain,
~ in(sK1,ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set))),
inference(superposition,[status(thm)],[c_93263,c_70]) ).
tcf(c_93786,plain,
! [X0: $i] :
( sP0(X0,sK24(sK1,empty_set),sK23(sK1,empty_set),relation_inverse(sK1))
| ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_93262,c_4838]) ).
tcf(c_93788,plain,
( ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( sK15(relation_inverse(sK1),sK23(sK1,empty_set)) = apply(sK1,sK23(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_93262,c_62859]) ).
tcf(c_93789,plain,
( ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_93262,c_59117]) ).
tcf(c_93790,plain,
( ( apply(sK2,sK24(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))) = sK23(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_93262,c_58270]) ).
tcf(c_94201,plain,
~ in(relation_inverse(sK1),ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set))),
inference(superposition,[status(thm)],[c_93267,c_70]) ).
tcf(c_94202,plain,
element(ordered_pair(sK24(sK1,empty_set),sK23(sK1,empty_set)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_93267,c_69]) ).
tcf(c_94204,plain,
( in(sK23(sK1,empty_set),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_93267,c_106]) ).
tcf(c_94209,plain,
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_94204,c_3821]) ).
tcf(c_94212,plain,
( in(ordered_pair(sK15(sK1,sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_93772,c_71817]) ).
tcf(c_94215,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_93772,c_64231]) ).
tcf(c_94216,plain,
( ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_93772,c_63810]) ).
tcf(c_94217,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_93772,c_60777]) ).
tcf(c_94228,plain,
( in(ordered_pair(sK23(sK1,empty_set),sK24(sK1,empty_set)),sK1)
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK23(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_94212,c_93258,c_93262,c_93769]) ).
tcf(c_94232,plain,
~ in(sK1,ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_39836,c_70]) ).
tcf(c_94233,plain,
element(ordered_pair(sK15(sK1,sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1),
inference(superposition,[status(thm)],[c_39836,c_69]) ).
tcf(c_94235,plain,
( in(sK21(sK1,empty_set),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_39836,c_106]) ).
tcf(c_94241,plain,
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_94235,c_4013]) ).
tcf(c_94258,plain,
apply(sK1,sK23(empty_set,sK1)) = sK24(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_24256,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801,c_39528]) ).
tcf(c_94260,plain,
apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK23(empty_set,sK1),
inference(demodulation,[status(thm)],[c_41214,c_94258]) ).
tcf(c_94261,plain,
sK15(relation_inverse(sK1),sK23(empty_set,sK1)) = sK24(empty_set,sK1),
inference(demodulation,[status(thm)],[c_41048,c_94258]) ).
tcf(c_94262,plain,
sK15(sK1,sK24(empty_set,sK1)) = sK23(empty_set,sK1),
inference(demodulation,[status(thm)],[c_40625,c_94260]) ).
tcf(c_94264,plain,
element(sK23(empty_set,sK1),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_40763,c_94262]) ).
tcf(c_94265,plain,
in(sK23(empty_set,sK1),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_40761,c_94262]) ).
tcf(c_94266,plain,
in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_40740,c_94262]) ).
tcf(c_94267,plain,
! [X0: $i] :
( sP0(X0,sK23(empty_set,sK1),sK24(empty_set,sK1),sK1)
| ~ in(sK23(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_94258,c_49]) ).
tcf(c_94268,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK23(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_94258,c_53]) ).
tcf(c_94269,plain,
! [X0: $i] :
( in(apply(sK1,sK23(empty_set,sK1)),relation_rng(sK1))
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK23(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_94258,c_52]) ).
tcf(c_94270,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ~ function(sK1)
| ~ relation(sK1)
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94258,c_87]) ).
tcf(c_94272,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94258,c_12599]) ).
tcf(c_94273,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94258,c_61586]) ).
tcf(c_94277,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = sK15(sK1,sK24(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_94258,c_56725]) ).
tcf(c_94278,plain,
( in(sK23(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_94258,c_54665]) ).
tcf(c_94279,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(apply(sK1,sK23(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_94258,c_54505]) ).
tcf(c_94280,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(empty_set,sK1)) = sK23(empty_set,sK1) )
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_94258,c_53757]) ).
tcf(c_94288,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94270,c_65,c_64]) ).
tcf(c_94291,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ( apply(sK2,sK24(empty_set,sK1)) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_94280,c_94258]) ).
tcf(c_94295,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_94272,c_94258]) ).
tcf(c_94299,plain,
! [X0: $i] :
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK23(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_94269,c_4013,c_94258]) ).
tcf(c_94300,plain,
( in(sK23(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_94278,c_94258]) ).
tcf(c_94301,plain,
( in(sK23(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94300,c_40617]) ).
tcf(c_94305,plain,
! [X0: $i] :
( ( apply(X0,sK24(empty_set,sK1)) = sK23(empty_set,sK1) )
| ~ in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK24(empty_set,sK1),sK23(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_94268,c_94258]) ).
tcf(c_94309,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_94279,c_94258]) ).
tcf(c_94310,plain,
( in(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_94309,c_40617]) ).
tcf(c_94431,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1)))) = apply(sK1,sK23(empty_set,sK1)),
inference(superposition,[status(thm)],[c_94265,c_12766]) ).
tcf(c_94432,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1)))) = sK7(sK1,sK23(empty_set,sK1)),
inference(superposition,[status(thm)],[c_94265,c_12765]) ).
tcf(c_94433,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1)))) = apply(sK1,sK23(empty_set,sK1)),
inference(superposition,[status(thm)],[c_94265,c_10203]) ).
tcf(c_94434,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1)))) = sK7(sK1,sK23(empty_set,sK1)),
inference(superposition,[status(thm)],[c_94265,c_10202]) ).
tcf(c_94435,plain,
apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = sK15(sK1,apply(sK1,sK23(empty_set,sK1))),
inference(superposition,[status(thm)],[c_94265,c_6249]) ).
tcf(c_94436,plain,
apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = sK15(sK1,sK7(sK1,sK23(empty_set,sK1))),
inference(superposition,[status(thm)],[c_94265,c_5349]) ).
tcf(c_94437,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_94265,c_4997]) ).
tcf(c_94441,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK24(empty_set,sK1)) = sK23(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_94437,c_94258]) ).
tcf(c_94444,plain,
sK15(sK1,sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_94436,c_41403]) ).
tcf(c_94447,plain,
sK7(sK1,sK23(empty_set,sK1)) = sK24(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_94432,c_41403,c_94258]) ).
tcf(c_94450,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ~ relation(sK1)
| ~ in(sK24(empty_set,sK1),relation_rng(sK1)) ),
inference(superposition,[status(thm)],[c_94262,c_107]) ).
tcf(c_94452,plain,
! [X0: $i] :
( sP0(X0,sK24(empty_set,sK1),sK23(empty_set,sK1),relation_inverse(sK1))
| ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_94262,c_4838]) ).
tcf(c_94454,plain,
( ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( sK15(relation_inverse(sK1),sK23(empty_set,sK1)) = apply(sK1,sK23(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_94262,c_62859]) ).
tcf(c_94455,plain,
( ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_94262,c_59117]) ).
tcf(c_94456,plain,
( ( apply(sK2,sK24(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))) = sK23(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_94262,c_58270]) ).
tcf(c_94458,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ( apply(relation_inverse(sK1),sK24(empty_set,sK1)) = empty_set ) ),
inference(superposition,[status(thm)],[c_94262,c_34537]) ).
tcf(c_94467,plain,
( in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1)
| ~ relation(sK1)
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_94450,c_4013]) ).
tcf(c_94468,plain,
in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_94467,c_64,c_40617]) ).
tcf(c_94476,plain,
~ in(sK1,ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1))),
inference(superposition,[status(thm)],[c_94468,c_70]) ).
tcf(c_94477,plain,
element(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),sK1),
inference(superposition,[status(thm)],[c_94468,c_69]) ).
tcf(c_94479,plain,
( in(sK24(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_94468,c_106]) ).
tcf(c_94482,plain,
( ( sK1 = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(ordered_pair(sK23(empty_set,sK1),sK24(empty_set,sK1)),empty_set) ),
inference(superposition,[status(thm)],[c_94468,c_129]) ).
tcf(c_94486,plain,
( in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_94479,c_4013]) ).
tcf(c_94518,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK23(relation_dom(X0),sK1))) = sK23(relation_dom(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94494,c_4997]) ).
tcf(c_94657,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_dom(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK23(sK1,relation_dom(X0)))) = sK23(sK1,relation_dom(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_94633,c_4997]) ).
tcf(c_95340,plain,
~ in(relation_inverse(sK1),ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1))),
inference(superposition,[status(thm)],[c_94266,c_70]) ).
tcf(c_95341,plain,
element(ordered_pair(sK24(empty_set,sK1),sK23(empty_set,sK1)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_94266,c_69]) ).
tcf(c_95343,plain,
( in(sK23(empty_set,sK1),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_94266,c_106]) ).
tcf(c_95348,plain,
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_95343,c_3821]) ).
tcf(c_95354,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94447,c_64231]) ).
tcf(c_95355,plain,
( ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_94447,c_63810]) ).
tcf(c_95356,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94447,c_60777]) ).
tcf(c_95370,plain,
~ in(sK1,ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_40374,c_70]) ).
tcf(c_95371,plain,
element(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1),
inference(superposition,[status(thm)],[c_40374,c_69]) ).
tcf(c_95373,plain,
( in(sK22(empty_set,sK1),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_40374,c_106]) ).
tcf(c_95379,plain,
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_95373,c_4013]) ).
tcf(c_95506,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK23(relation_rng(X0),sK1))) = sK23(relation_rng(X0),sK1) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95481,c_4997]) ).
tcf(c_95779,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK23(sK1,relation_rng(X0)))) = sK23(sK1,relation_rng(X0)) )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_95754,c_4997]) ).
tcf(c_95921,plain,
( ~ in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ~ in(relation_inverse(sK1),ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2))))) ),
inference(superposition,[status(thm)],[c_32021,c_70]) ).
tcf(c_95922,plain,
( element(ordered_pair(sK20(relation_dom(sK2)),sK15(sK1,sK20(relation_dom(sK2)))),relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32021,c_69]) ).
tcf(c_95924,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32021,c_106]) ).
tcf(c_95925,plain,
( in(sK20(relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32021,c_78]) ).
tcf(c_95927,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ~ relation(sK1)
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32021,c_297]) ).
tcf(c_95932,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_95924,c_3821]) ).
tcf(c_95933,plain,
( in(sK15(sK1,sK20(relation_dom(sK2))),relation_dom(sK1))
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95932,c_3611]) ).
tcf(c_95939,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_25205,c_136,c_2037,c_4013,c_4017,c_4147,c_5811,c_16946,c_19508,c_25205,c_30801]) ).
tcf(c_95940,plain,
( ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(renaming,[status(thm)],[c_95939]) ).
tcf(c_95945,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,empty_set),empty_set,sK2)
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_95940,c_49]) ).
tcf(c_95946,plain,
! [X0: $i] :
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ( apply(X0,apply(sK2,sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_95940,c_53]) ).
tcf(c_95947,plain,
! [X0: $i] :
( in(apply(sK2,sK21(sK1,empty_set)),relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_95940,c_52]) ).
tcf(c_95950,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_95940,c_19430]) ).
tcf(c_95951,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_95940,c_4045]) ).
tcf(c_95952,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_95940,c_19431]) ).
tcf(c_95953,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_95940,c_18734]) ).
tcf(c_95954,plain,
( in(ordered_pair(sK21(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_95940,c_87]) ).
tcf(c_95958,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95953,c_39669]) ).
tcf(c_95962,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95952,c_39669]) ).
tcf(c_95966,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95951,c_39669]) ).
tcf(c_95970,plain,
( in(ordered_pair(sK21(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95954,c_62,c_61,c_39669]) ).
tcf(c_95973,plain,
! [X0: $i] :
( in(apply(sK2,sK21(sK1,empty_set)),relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ sP0(sK2,empty_set,sK21(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95947,c_39669]) ).
tcf(c_95977,plain,
! [X0: $i] :
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ( apply(X0,apply(sK2,sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ sP0(sK2,empty_set,sK21(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95946,c_39669]) ).
tcf(c_96211,plain,
~ in(sK1,ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set)))),
inference(superposition,[status(thm)],[c_40774,c_70]) ).
tcf(c_96212,plain,
element(ordered_pair(sK22(sK1,empty_set),apply(sK1,sK22(sK1,empty_set))),sK1),
inference(superposition,[status(thm)],[c_40774,c_69]) ).
tcf(c_96214,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_rng(sK1))
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_40774,c_106]) ).
tcf(c_96220,plain,
( in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2))
| ~ relation(sK1) ),
inference(light_normalisation,[status(thm)],[c_96214,c_4013]) ).
tcf(c_96228,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,empty_set),sK5(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK6(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_89646,c_49]) ).
tcf(c_96229,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89646,c_53]) ).
tcf(c_96230,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK6(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_89646,c_52]) ).
tcf(c_96247,plain,
! [X0: $i] :
( in(sK5(sK1,empty_set),relation_dom(sK1))
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_96230,c_3821,c_4030,c_89646]) ).
tcf(c_96248,plain,
! [X0: $i] :
( ( apply(X0,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_96229,c_4030,c_89646]) ).
tcf(c_96249,plain,
! [X0: $i] :
( ( apply(X0,sK5(sK1,empty_set)) = sK6(sK1,empty_set) )
| ~ sP0(relation_inverse(sK1),sK5(sK1,empty_set),sK6(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96248,c_32119]) ).
tcf(c_96257,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(sK2,ordered_pair(sK21(sK1,empty_set),empty_set)) ),
inference(superposition,[status(thm)],[c_95970,c_70]) ).
tcf(c_96258,plain,
( element(ordered_pair(sK21(sK1,empty_set),empty_set),sK2)
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_95970,c_69]) ).
tcf(c_96260,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_95970,c_106]) ).
tcf(c_96265,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96260,c_61]) ).
tcf(c_96277,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(relation_rng(sK2),empty_set) ),
inference(superposition,[status(thm)],[c_96265,c_70]) ).
tcf(c_96278,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_96265,c_69]) ).
tcf(c_96280,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ( apply(sK2,sK7(relation_inverse(sK2),empty_set)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_96265,c_43161]) ).
tcf(c_96300,plain,
in(ordered_pair(sK6(sK1,empty_set),sK15(sK1,sK6(sK1,empty_set))),relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_32098,c_136,c_2037,c_4013,c_4017,c_4154,c_4147,c_5796,c_8128,c_16946,c_19508,c_30801,c_32098]) ).
tcf(c_96310,plain,
sK15(sK1,sK21(sK1,empty_set)) = sK22(sK1,empty_set),
inference(global_subsumption_just,[status(thm)],[c_25207,c_136,c_2037,c_4013,c_4017,c_4147,c_5811,c_16946,c_19508,c_30801,c_39678]) ).
tcf(c_96312,plain,
element(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1),
inference(demodulation,[status(thm)],[c_94233,c_96310]) ).
tcf(c_96313,plain,
in(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1),
inference(demodulation,[status(thm)],[c_39836,c_96310]) ).
tcf(c_96317,plain,
in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_39846,c_96310]) ).
tcf(c_96318,plain,
apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK22(sK1,empty_set),
inference(demodulation,[status(thm)],[c_39677,c_96310]) ).
tcf(c_96319,plain,
apply(sK1,sK22(sK1,empty_set)) = sK21(sK1,empty_set),
inference(demodulation,[status(thm)],[c_39713,c_96310]) ).
tcf(c_96328,plain,
sK15(relation_inverse(sK1),sK22(sK1,empty_set)) = sK21(sK1,empty_set),
inference(demodulation,[status(thm)],[c_40659,c_96319]) ).
tcf(c_96331,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,empty_set),sK22(sK1,empty_set),relation_inverse(sK1))
| ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_96310,c_4838]) ).
tcf(c_96333,plain,
( ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( sK15(relation_inverse(sK1),sK22(sK1,empty_set)) = apply(sK1,sK22(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_96310,c_62859]) ).
tcf(c_96334,plain,
( ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_96310,c_59117]) ).
tcf(c_96335,plain,
( ( apply(sK2,sK21(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_96310,c_58270]) ).
tcf(c_96561,plain,
~ in(sK1,ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set))),
inference(superposition,[status(thm)],[c_96313,c_70]) ).
tcf(c_96567,plain,
( ( relation_inverse(sK1) = empty_set )
| ~ relation(empty_set)
| ~ relation(sK1)
| ~ in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),empty_set) ),
inference(superposition,[status(thm)],[c_96313,c_124]) ).
tcf(c_96571,plain,
~ in(relation_inverse(sK1),ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set))),
inference(superposition,[status(thm)],[c_96317,c_70]) ).
tcf(c_96572,plain,
element(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_96317,c_69]) ).
tcf(c_96579,plain,
! [X0: $i] :
( sP0(X0,sK22(sK1,empty_set),sK21(sK1,empty_set),sK1)
| ~ in(sK22(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_96319,c_49]) ).
tcf(c_96580,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK22(sK1,empty_set))) = sK22(sK1,empty_set) )
| ~ in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK22(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_96319,c_53]) ).
tcf(c_96581,plain,
! [X0: $i] :
( in(apply(sK1,sK22(sK1,empty_set)),relation_rng(sK1))
| ~ in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK22(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_96319,c_52]) ).
tcf(c_96585,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_96319,c_61586]) ).
tcf(c_96589,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( apply(relation_inverse(sK1),sK21(sK1,empty_set)) = sK15(sK1,sK21(sK1,empty_set)) ) ),
inference(superposition,[status(thm)],[c_96319,c_56725]) ).
tcf(c_96591,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(apply(sK1,sK22(sK1,empty_set)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_96319,c_54505]) ).
tcf(c_96592,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set ) ),
inference(superposition,[status(thm)],[c_96319,c_53757]) ).
tcf(c_96600,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ( apply(sK2,sK21(sK1,empty_set)) = sK22(sK1,empty_set) ) ),
inference(light_normalisation,[status(thm)],[c_96592,c_96319]) ).
tcf(c_96604,plain,
! [X0: $i] :
( in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK22(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_96581,c_4013,c_96319]) ).
tcf(c_96605,plain,
! [X0: $i] :
( ( apply(X0,sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ~ in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,empty_set),sK22(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_96580,c_96319]) ).
tcf(c_96606,plain,
! [X0: $i] :
( ( apply(X0,sK21(sK1,empty_set)) = sK22(sK1,empty_set) )
| ~ sP0(sK1,sK21(sK1,empty_set),sK22(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96605,c_40653]) ).
tcf(c_96609,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_96591,c_96319]) ).
tcf(c_96610,plain,
( in(ordered_pair(sK21(sK1,empty_set),sK22(sK1,empty_set)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96609,c_39669]) ).
tcf(c_96642,plain,
( ~ in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ~ in(relation_inverse(sK1),ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1)))) ),
inference(superposition,[status(thm)],[c_34146,c_70]) ).
tcf(c_96643,plain,
( element(ordered_pair(apply(sK1,sK20(relation_dom(sK1))),sK20(relation_dom(sK1))),relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34146,c_69]) ).
tcf(c_96645,plain,
( in(sK20(relation_dom(sK1)),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34146,c_106]) ).
tcf(c_96646,plain,
( in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34146,c_78]) ).
tcf(c_96648,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ~ relation(sK1)
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34146,c_297]) ).
tcf(c_96653,plain,
( in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ relation(relation_inverse(sK1))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_96646,c_4030]) ).
tcf(c_96654,plain,
( in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2))
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_96653,c_3611]) ).
tcf(c_96704,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_34158]) ).
tcf(c_96705,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),sK7(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34715,c_33908]) ).
tcf(c_96945,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_34158]) ).
tcf(c_96946,plain,
( in(sK20(relation_dom(sK2)),relation_dom(sK2))
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))) = empty_set ) ),
inference(superposition,[status(thm)],[c_34718,c_33908]) ).
tcf(c_97339,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set ) ),
inference(global_subsumption_just,[status(thm)],[c_26654,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19508,c_26654,c_30801]) ).
tcf(c_97340,plain,
( ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(renaming,[status(thm)],[c_97339]) ).
tcf(c_97345,plain,
! [X0: $i] :
( sP0(X0,sK22(empty_set,sK1),empty_set,sK2)
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_97340,c_49]) ).
tcf(c_97346,plain,
! [X0: $i] :
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ( apply(X0,apply(sK2,sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_97340,c_53]) ).
tcf(c_97347,plain,
! [X0: $i] :
( in(apply(sK2,sK22(empty_set,sK1)),relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_97340,c_52]) ).
tcf(c_97350,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(relation_rng(sK2),empty_set)
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_97340,c_19430]) ).
tcf(c_97351,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_97340,c_4045]) ).
tcf(c_97352,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_97340,c_19431]) ).
tcf(c_97353,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(relation_inverse(sK2))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_97340,c_18734]) ).
tcf(c_97354,plain,
( in(ordered_pair(sK22(empty_set,sK1),empty_set),sK2)
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ function(sK2)
| ~ relation(sK2)
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_97340,c_87]) ).
tcf(c_97358,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97353,c_40094]) ).
tcf(c_97362,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97352,c_40094]) ).
tcf(c_97366,plain,
( in(empty_set,relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97351,c_40094]) ).
tcf(c_97370,plain,
( in(ordered_pair(sK22(empty_set,sK1),empty_set),sK2)
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97354,c_62,c_61,c_40094]) ).
tcf(c_97373,plain,
! [X0: $i] :
( in(apply(sK2,sK22(empty_set,sK1)),relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ sP0(sK2,empty_set,sK22(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97347,c_40094]) ).
tcf(c_97377,plain,
! [X0: $i] :
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ( apply(X0,apply(sK2,sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ sP0(sK2,empty_set,sK22(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97346,c_40094]) ).
tcf(c_98959,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(sK2,ordered_pair(sK22(empty_set,sK1),empty_set)) ),
inference(superposition,[status(thm)],[c_97370,c_70]) ).
tcf(c_98960,plain,
( element(ordered_pair(sK22(empty_set,sK1),empty_set),sK2)
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_97370,c_69]) ).
tcf(c_98962,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ relation(sK2) ),
inference(superposition,[status(thm)],[c_97370,c_106]) ).
tcf(c_98967,plain,
( in(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_98962,c_61]) ).
tcf(c_98979,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(relation_rng(sK2),empty_set) ),
inference(superposition,[status(thm)],[c_98967,c_70]) ).
tcf(c_98980,plain,
( element(empty_set,relation_rng(sK2))
| ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_98967,c_69]) ).
tcf(c_98982,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ( apply(sK2,sK7(relation_inverse(sK2),empty_set)) = empty_set )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_98967,c_43161]) ).
tcf(c_99016,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,relation_rng(sK2)) = empty_set )
| ( apply(sK1,relation_dom(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK2))) = empty_set )
| ( apply(sK1,sK15(sK1,relation_rng(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_38530]) ).
tcf(c_99056,plain,
! [X0: $i] :
( sP0(X0,relation_dom(sK2),empty_set,sK2)
| ~ in(relation_dom(sK2),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_99052,c_49]) ).
tcf(c_99057,plain,
! [X0: $i] :
( ( apply(X0,apply(sK2,relation_dom(sK2))) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_99052,c_53]) ).
tcf(c_99058,plain,
! [X0: $i] :
( in(apply(sK2,relation_dom(sK2)),relation_rng(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(superposition,[status(thm)],[c_99052,c_52]) ).
tcf(c_99080,plain,
! [X0: $i] :
( in(empty_set,relation_rng(sK2))
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_99058,c_99052]) ).
tcf(c_99084,plain,
! [X0: $i] :
( ( apply(X0,empty_set) = relation_dom(sK2) )
| ~ in(relation_dom(sK2),relation_dom(sK2))
| ~ sP0(sK2,empty_set,relation_dom(sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_99057,c_99052]) ).
tcf(c_99133,plain,
sK15(sK1,sK22(empty_set,sK1)) = sK21(empty_set,sK1),
inference(global_subsumption_just,[status(thm)],[c_26656,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_16946,c_19508,c_30801,c_40102]) ).
tcf(c_99135,plain,
element(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1),
inference(demodulation,[status(thm)],[c_95371,c_99133]) ).
tcf(c_99136,plain,
in(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1),
inference(demodulation,[status(thm)],[c_40374,c_99133]) ).
tcf(c_99138,plain,
element(sK21(empty_set,sK1),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_40608,c_99133]) ).
tcf(c_99139,plain,
in(sK21(empty_set,sK1),relation_dom(sK1)),
inference(demodulation,[status(thm)],[c_40406,c_99133]) ).
tcf(c_99140,plain,
in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),relation_inverse(sK1)),
inference(demodulation,[status(thm)],[c_40384,c_99133]) ).
tcf(c_99141,plain,
apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK21(empty_set,sK1),
inference(demodulation,[status(thm)],[c_40101,c_99133]) ).
tcf(c_99142,plain,
apply(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1),
inference(demodulation,[status(thm)],[c_40105,c_99133]) ).
tcf(c_99144,plain,
sK15(relation_inverse(sK1),sK21(empty_set,sK1)) = sK22(empty_set,sK1),
inference(demodulation,[status(thm)],[c_41464,c_99142]) ).
tcf(c_99147,plain,
! [X0: $i] :
( sP0(X0,sK22(empty_set,sK1),sK21(empty_set,sK1),relation_inverse(sK1))
| ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_99133,c_4838]) ).
tcf(c_99149,plain,
( ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( sK15(relation_inverse(sK1),sK21(empty_set,sK1)) = apply(sK1,sK21(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_99133,c_62859]) ).
tcf(c_99151,plain,
( ( apply(sK2,sK22(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_99133,c_58270]) ).
tcf(c_99256,plain,
apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1)))) = apply(sK1,sK21(empty_set,sK1)),
inference(superposition,[status(thm)],[c_99139,c_12766]) ).
tcf(c_99257,plain,
apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1)))) = sK7(sK1,sK21(empty_set,sK1)),
inference(superposition,[status(thm)],[c_99139,c_12765]) ).
tcf(c_99258,plain,
apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1)))) = apply(sK1,sK21(empty_set,sK1)),
inference(superposition,[status(thm)],[c_99139,c_10203]) ).
tcf(c_99259,plain,
apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1)))) = sK7(sK1,sK21(empty_set,sK1)),
inference(superposition,[status(thm)],[c_99139,c_10202]) ).
tcf(c_99260,plain,
apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))) = sK15(sK1,apply(sK1,sK21(empty_set,sK1))),
inference(superposition,[status(thm)],[c_99139,c_6249]) ).
tcf(c_99261,plain,
apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))) = sK15(sK1,sK7(sK1,sK21(empty_set,sK1))),
inference(superposition,[status(thm)],[c_99139,c_5349]) ).
tcf(c_99262,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_99139,c_4997]) ).
tcf(c_99266,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,sK22(empty_set,sK1)) = sK21(empty_set,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_99262,c_99142]) ).
tcf(c_99269,plain,
sK15(sK1,sK7(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_99261,c_41530]) ).
tcf(c_99272,plain,
sK7(sK1,sK21(empty_set,sK1)) = sK22(empty_set,sK1),
inference(light_normalisation,[status(thm)],[c_99257,c_41530,c_99142]) ).
tcf(c_99276,plain,
~ in(sK1,ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1))),
inference(superposition,[status(thm)],[c_99136,c_70]) ).
tcf(c_99296,plain,
in(ordered_pair(apply(sK1,sK23(sK1,empty_set)),sK23(sK1,empty_set)),relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_40928,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_8873,c_16946,c_19508,c_30801,c_40928]) ).
tcf(c_99299,plain,
in(ordered_pair(apply(sK1,sK23(empty_set,sK1)),sK23(empty_set,sK1)),relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_41055,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_8992,c_16946,c_19508,c_30801,c_41055]) ).
tcf(c_99302,plain,
in(ordered_pair(apply(sK1,sK21(empty_set,sK1)),sK21(empty_set,sK1)),relation_inverse(sK1)),
inference(global_subsumption_just,[status(thm)],[c_41471,c_136,c_145,c_2037,c_3992,c_4013,c_4017,c_4147,c_9083,c_16946,c_19508,c_30801,c_41471]) ).
tcf(c_99305,plain,
( in(sK5(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_54928,c_89697]) ).
tcf(c_99316,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(relation_rng(sK2),sK5(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_99305,c_70]) ).
tcf(c_99317,plain,
( element(sK5(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_99305,c_69]) ).
tcf(c_99319,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK6(sK1,empty_set) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK5(sK1,empty_set))) = sK5(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_99305,c_43161]) ).
tcf(c_99330,plain,
( in(sK22(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_54929,c_96319]) ).
tcf(c_99341,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(relation_rng(sK2),sK22(sK1,empty_set)) ),
inference(superposition,[status(thm)],[c_99330,c_70]) ).
tcf(c_99342,plain,
( element(sK22(sK1,empty_set),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(superposition,[status(thm)],[c_99330,c_69]) ).
tcf(c_99344,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK21(sK1,empty_set) = empty_set )
| ( apply(sK2,sK7(relation_inverse(sK2),sK22(sK1,empty_set))) = sK22(sK1,empty_set) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_99330,c_43161]) ).
tcf(c_99953,plain,
~ in(relation_inverse(sK1),ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1))),
inference(superposition,[status(thm)],[c_99140,c_70]) ).
tcf(c_99954,plain,
element(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),relation_inverse(sK1)),
inference(superposition,[status(thm)],[c_99140,c_69]) ).
tcf(c_99956,plain,
( in(sK21(empty_set,sK1),relation_rng(relation_inverse(sK1)))
| ~ relation(relation_inverse(sK1)) ),
inference(superposition,[status(thm)],[c_99140,c_106]) ).
tcf(c_99961,plain,
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ relation(relation_inverse(sK1)) ),
inference(light_normalisation,[status(thm)],[c_99956,c_3821]) ).
tcf(c_99962,plain,
! [X0: $i] :
( sP0(X0,sK21(empty_set,sK1),sK22(empty_set,sK1),sK1)
| ~ in(sK21(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_99142,c_49]) ).
tcf(c_99963,plain,
! [X0: $i] :
( ( apply(X0,apply(sK1,sK21(empty_set,sK1))) = sK21(empty_set,sK1) )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK21(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_99142,c_53]) ).
tcf(c_99964,plain,
! [X0: $i] :
( in(apply(sK1,sK21(empty_set,sK1)),relation_rng(sK1))
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK21(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_99142,c_52]) ).
tcf(c_99968,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_99142,c_61586]) ).
tcf(c_99972,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( apply(relation_inverse(sK1),sK22(empty_set,sK1)) = sK15(sK1,sK22(empty_set,sK1)) ) ),
inference(superposition,[status(thm)],[c_99142,c_56725]) ).
tcf(c_99973,plain,
( in(sK21(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99142,c_54665]) ).
tcf(c_99974,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(apply(sK1,sK21(empty_set,sK1)),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_99142,c_54505]) ).
tcf(c_99983,plain,
! [X0: $i] :
( in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK21(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_99964,c_4013,c_99142]) ).
tcf(c_99984,plain,
( in(sK21(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_99973,c_99142]) ).
tcf(c_99985,plain,
( in(sK21(empty_set,sK1),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99984,c_40094]) ).
tcf(c_99989,plain,
! [X0: $i] :
( ( apply(X0,sK22(empty_set,sK1)) = sK21(empty_set,sK1) )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ sP0(sK1,sK22(empty_set,sK1),sK21(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_99963,c_99142]) ).
tcf(c_99990,plain,
! [X0: $i] :
( ( apply(X0,sK22(empty_set,sK1)) = sK21(empty_set,sK1) )
| ~ sP0(sK1,sK22(empty_set,sK1),sK21(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99989,c_99139]) ).
tcf(c_99993,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_99974,c_99142]) ).
tcf(c_99994,plain,
( in(ordered_pair(sK22(empty_set,sK1),sK21(empty_set,sK1)),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_99993,c_40094]) ).
tcf(c_100003,plain,
( in(ordered_pair(sK15(sK1,sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(sK15(sK1,sK7(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_99272,c_71817]) ).
tcf(c_100004,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( apply(sK1,sK15(sK1,sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_99272,c_64168]) ).
tcf(c_100006,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_99272,c_64231]) ).
tcf(c_100007,plain,
( ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_99272,c_63810]) ).
tcf(c_100008,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(sK7(relation_inverse(sK1),sK7(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_99272,c_60777]) ).
tcf(c_100020,plain,
( in(ordered_pair(sK21(empty_set,sK1),sK22(empty_set,sK1)),sK1)
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK21(empty_set,sK1),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100003,c_99133,c_99142,c_99269]) ).
tcf(c_100038,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_rng(sK2)) = empty_set )
| ( apply(sK2,sK7(sK1,relation_rng(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_56485]) ).
tcf(c_100062,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,relation_dom(sK1)),empty_set,sK2)
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_100034,c_49]) ).
tcf(c_100063,plain,
! [X0: $i] :
( ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(X0,apply(sK2,sK7(sK1,relation_dom(sK1)))) = sK7(sK1,relation_dom(sK1)) )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,relation_dom(sK1)),X0) ),
inference(superposition,[status(thm)],[c_100034,c_53]) ).
tcf(c_100064,plain,
! [X0: $i] :
( in(apply(sK2,sK7(sK1,relation_dom(sK1))),relation_rng(sK2))
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ~ in(sK7(sK1,relation_dom(sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,relation_dom(sK1)),X0) ),
inference(superposition,[status(thm)],[c_100034,c_52]) ).
tcf(c_100201,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,relation_dom(sK1)) = empty_set )
| ( apply(sK1,relation_rng(sK2)) = empty_set )
| ( apply(sK2,apply(sK1,relation_dom(sK1))) = empty_set )
| ( apply(sK2,apply(sK1,relation_rng(sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_58008]) ).
tcf(c_100466,plain,
! [X0: $i] :
( sP0(X0,sK24(sK1,empty_set),sK23(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK24(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_93260,c_49]) ).
tcf(c_100467,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_93260,c_53]) ).
tcf(c_100468,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK24(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_93260,c_52]) ).
tcf(c_100485,plain,
! [X0: $i] :
( in(sK23(sK1,empty_set),relation_dom(sK1))
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_100468,c_3821,c_4030,c_93260]) ).
tcf(c_100486,plain,
! [X0: $i] :
( ( apply(X0,sK23(sK1,empty_set)) = sK24(sK1,empty_set) )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_100467,c_4030,c_93260]) ).
tcf(c_100487,plain,
! [X0: $i] :
( ( apply(X0,sK23(sK1,empty_set)) = sK24(sK1,empty_set) )
| ~ sP0(relation_inverse(sK1),sK23(sK1,empty_set),sK24(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100486,c_39295]) ).
tcf(c_100497,plain,
! [X0: $i] :
( sP0(X0,sK24(empty_set,sK1),sK23(empty_set,sK1),relation_inverse(sK1))
| ~ in(sK24(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_94260,c_49]) ).
tcf(c_100498,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_94260,c_53]) ).
tcf(c_100499,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK24(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ in(sK24(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_94260,c_52]) ).
tcf(c_100516,plain,
! [X0: $i] :
( in(sK23(empty_set,sK1),relation_dom(sK1))
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_100499,c_3821,c_4030,c_94260]) ).
tcf(c_100517,plain,
! [X0: $i] :
( ( apply(X0,sK23(empty_set,sK1)) = sK24(empty_set,sK1) )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_100498,c_4030,c_94260]) ).
tcf(c_100518,plain,
! [X0: $i] :
( ( apply(X0,sK23(empty_set,sK1)) = sK24(empty_set,sK1) )
| ~ sP0(relation_inverse(sK1),sK23(empty_set,sK1),sK24(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100517,c_40617]) ).
tcf(c_100536,plain,
( ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_89697,c_64920]) ).
tcf(c_100540,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_33899,c_64920]) ).
tcf(c_100546,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK6(sK1,empty_set))) = sK6(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_32125,c_64920]) ).
tcf(c_100550,plain,
( ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK20(relation_dom(sK2)))) = sK20(relation_dom(sK2)) ) ),
inference(superposition,[status(thm)],[c_34151,c_64920]) ).
tcf(c_100551,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(sK1,empty_set))) = sK24(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_39302,c_64920]) ).
tcf(c_100552,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK24(empty_set,sK1))) = sK24(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40624,c_64920]) ).
tcf(c_100556,plain,
( ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_96319,c_64920]) ).
tcf(c_100558,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) ) ),
inference(superposition,[status(thm)],[c_39676,c_64920]) ).
tcf(c_100559,plain,
( ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) ) ),
inference(superposition,[status(thm)],[c_40100,c_64920]) ).
tcf(c_100560,plain,
! [X0: $i,X1: $i] :
( sP0(X1,apply(relation_inverse(sK1),apply(sK1,X0)),apply(sK1,X0),sK1)
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_rng(X1)) ),
inference(superposition,[status(thm)],[c_64920,c_49]) ).
tcf(c_100561,plain,
! [X0: $i,X1: $i] :
( ( apply(sK1,X0) = empty_set )
| ( apply(X1,apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0)))) = apply(relation_inverse(sK1),apply(sK1,X0)) )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),apply(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_64920,c_53]) ).
tcf(c_100562,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))),relation_rng(sK1))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),apply(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(superposition,[status(thm)],[c_64920,c_52]) ).
tcf(c_100571,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,X0),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64920,c_54665]) ).
tcf(c_100572,plain,
! [X0: $i] :
( in(ordered_pair(apply(sK1,X0),apply(relation_inverse(sK1),apply(sK1,X0))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_64920,c_54505]) ).
tcf(c_100573,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,X0) = empty_set )
| ( apply(relation_inverse(sK1),apply(sK1,X0)) = apply(sK2,apply(sK1,X0)) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))) = empty_set ) ),
inference(superposition,[status(thm)],[c_64920,c_53757]) ).
tcf(c_100656,plain,
! [X0: $i,X1: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),apply(sK1,X0))),relation_dom(sK2))
| ( apply(sK1,X0) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,X0)),relation_dom(sK1))
| ~ sP0(sK1,apply(sK1,X0),apply(relation_inverse(sK1),apply(sK1,X0)),X1) ),
inference(light_normalisation,[status(thm)],[c_100562,c_4013]) ).
tcf(c_100758,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK1,sK20(relation_dom(sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK20(relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32039,c_100631]) ).
tcf(c_100764,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK13(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_59821,c_100631]) ).
tcf(c_100765,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK5(empty_set,relation_dom(sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_68397,c_100631]) ).
tcf(c_100807,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK5(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK5(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_89697,c_100631]) ).
tcf(c_100811,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_33899,c_100631]) ).
tcf(c_100817,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_32125,c_100631]) ).
tcf(c_100830,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_34151,c_100631]) ).
tcf(c_100831,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39302,c_100631]) ).
tcf(c_100832,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40624,c_100631]) ).
tcf(c_100833,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK23(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK23(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_93258,c_100631]) ).
tcf(c_100834,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK23(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK23(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_94258,c_100631]) ).
tcf(c_100835,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK21(empty_set,sK1)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK21(empty_set,sK1))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_99142,c_100631]) ).
tcf(c_100836,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK22(sK1,empty_set)) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK22(sK1,empty_set))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_96319,c_100631]) ).
tcf(c_100838,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_39676,c_100631]) ).
tcf(c_100839,plain,
( in(ordered_pair(apply(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1)))),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_40100,c_100631]) ).
tcf(c_100863,plain,
( in(ordered_pair(sK20(relation_dom(sK1)),apply(sK1,sK20(relation_dom(sK1)))),sK1)
| ( apply(sK1,sK20(relation_dom(sK1))) = empty_set )
| ~ in(sK20(relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100758,c_32039]) ).
tcf(c_100867,plain,
( in(ordered_pair(sK22(sK1,empty_set),sK21(sK1,empty_set)),sK1)
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK22(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100836,c_96318,c_96319]) ).
tcf(c_100871,plain,
( in(ordered_pair(sK5(sK1,empty_set),sK6(sK1,empty_set)),sK1)
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK5(sK1,empty_set),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100807,c_89646,c_89697]) ).
tcf(c_100876,plain,
( in(ordered_pair(sK5(empty_set,relation_dom(sK1)),apply(sK1,sK5(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK5(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100765,c_68397]) ).
tcf(c_100880,plain,
( in(ordered_pair(sK13(empty_set,relation_dom(sK1)),apply(sK1,sK13(empty_set,relation_dom(sK1)))),sK1)
| ( apply(sK1,sK13(empty_set,relation_dom(sK1))) = empty_set )
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100764,c_59821]) ).
tcf(c_100912,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(relation_inverse(sK1),apply(sK1,apply(sK2,sK20(relation_dom(sK2))))),relation_dom(sK1)) ),
inference(light_normalisation,[status(thm)],[c_100804,c_32001]) ).
tcf(c_101658,plain,
( in(sK23(sK1,relation_inverse(sK1)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK24(sK1,relation_inverse(sK1)))) = sK24(sK1,relation_inverse(sK1)) ) ),
inference(superposition,[status(thm)],[c_85387,c_4997]) ).
tcf(c_102135,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,empty_set),sK22(sK1,empty_set),relation_inverse(sK1))
| ~ in(sK21(sK1,empty_set),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_96318,c_49]) ).
tcf(c_102136,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,empty_set))) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_96318,c_53]) ).
tcf(c_102137,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,empty_set)),relation_rng(relation_inverse(sK1)))
| ~ in(sK21(sK1,empty_set),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(superposition,[status(thm)],[c_96318,c_52]) ).
tcf(c_102154,plain,
! [X0: $i] :
( in(sK22(sK1,empty_set),relation_dom(sK1))
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_102137,c_3821,c_4030,c_96318]) ).
tcf(c_102155,plain,
! [X0: $i] :
( ( apply(X0,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(light_normalisation,[status(thm)],[c_102136,c_4030,c_96318]) ).
tcf(c_102156,plain,
! [X0: $i] :
( ( apply(X0,sK22(sK1,empty_set)) = sK21(sK1,empty_set) )
| ~ sP0(relation_inverse(sK1),sK22(sK1,empty_set),sK21(sK1,empty_set),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102155,c_39669]) ).
tcf(c_102174,plain,
! [X0: $i] :
( sP0(X0,sK22(empty_set,sK1),sK21(empty_set,sK1),relation_inverse(sK1))
| ~ in(sK22(empty_set,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_99141,c_49]) ).
tcf(c_102175,plain,
! [X0: $i] :
( ( apply(X0,apply(relation_inverse(sK1),sK22(empty_set,sK1))) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_99141,c_53]) ).
tcf(c_102176,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(empty_set,sK1)),relation_rng(relation_inverse(sK1)))
| ~ in(sK22(empty_set,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(superposition,[status(thm)],[c_99141,c_52]) ).
tcf(c_102193,plain,
! [X0: $i] :
( in(sK21(empty_set,sK1),relation_dom(sK1))
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_102176,c_3821,c_4030,c_99141]) ).
tcf(c_102194,plain,
! [X0: $i] :
( ( apply(X0,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_102175,c_4030,c_99141]) ).
tcf(c_102195,plain,
! [X0: $i] :
( ( apply(X0,sK21(empty_set,sK1)) = sK22(empty_set,sK1) )
| ~ sP0(relation_inverse(sK1),sK21(empty_set,sK1),sK22(empty_set,sK1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102194,c_40094]) ).
tcf(c_102298,plain,
( in(sK23(relation_inverse(sK1),sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK24(relation_inverse(sK1),sK1))) = sK24(relation_inverse(sK1),sK1) ) ),
inference(superposition,[status(thm)],[c_86834,c_4997]) ).
tcf(c_102688,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_6673,c_4997]) ).
tcf(c_102772,plain,
( in(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102688,c_64]) ).
tcf(c_103052,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_28868,c_4838]) ).
tcf(c_103541,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,sK7(relation_inverse(sK1),X0))) = sK7(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_10129,c_4997]) ).
tcf(c_103669,plain,
( in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_57555,c_12272]) ).
tcf(c_103670,plain,
( in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2))
| ~ in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1)) ),
inference(superposition,[status(thm)],[c_67249,c_12272]) ).
tcf(c_103788,plain,
( in(sK20(relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK20(relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32039,c_12688]) ).
tcf(c_103818,plain,
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_59821,c_12688]) ).
tcf(c_103819,plain,
( in(sK13(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK13(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_61669,c_12688]) ).
tcf(c_103821,plain,
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(apply(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_68397,c_12688]) ).
tcf(c_103822,plain,
( in(sK5(empty_set,relation_dom(sK1)),relation_dom(sK1))
| ~ in(sK7(sK1,sK5(empty_set,relation_dom(sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_69366,c_12688]) ).
tcf(c_103835,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(sK2,apply(sK1,apply(relation_inverse(sK1),X0))) = apply(relation_inverse(sK1),X0) )
| ~ in(X0,relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_12688,c_4997]) ).
tcf(c_104428,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ in(relation_dom(sK2),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_102772,c_70]) ).
tcf(c_104429,plain,
( element(sK21(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102772,c_69]) ).
tcf(c_104432,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK1))) = apply(sK1,sK15(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_102772,c_12335]) ).
tcf(c_104433,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102772,c_8396]) ).
tcf(c_104434,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK21(sK1,sK1)))) = sK15(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_102772,c_8395]) ).
tcf(c_104435,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(sK2,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102772,c_4044]) ).
tcf(c_104436,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK21(sK1,sK1)) = apply(sK2,sK21(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_102772,c_42224]) ).
tcf(c_104437,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102772,c_12701]) ).
tcf(c_104438,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102772,c_10144]) ).
tcf(c_104439,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK15(sK1,sK21(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_102772,c_4468]) ).
tcf(c_104690,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK21(sK1,sK1)),empty_set,sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_29377,c_49]) ).
tcf(c_104691,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(X0,apply(sK2,sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_29377,c_53]) ).
tcf(c_104692,plain,
! [X0: $i] :
( in(apply(sK2,sK7(sK1,sK21(sK1,sK1))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK21(sK1,sK1)) = sK7(sK1,sK21(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK21(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_29377,c_52]) ).
tcf(c_105616,plain,
! [X0: $i] :
( sP0(X0,apply(sK2,sK21(sK1,sK2)),sK21(sK1,sK2),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_102954,c_49]) ).
tcf(c_105617,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(sK1,apply(sK2,sK21(sK1,sK2)))) = apply(sK2,sK21(sK1,sK2)) )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(sK2,sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102954,c_53]) ).
tcf(c_105618,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK21(sK1,sK2))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(sK2,sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102954,c_52]) ).
tcf(c_105629,plain,
( in(apply(sK2,sK21(sK1,sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102954,c_54665]) ).
tcf(c_105630,plain,
( in(ordered_pair(sK21(sK1,sK2),apply(sK2,sK21(sK1,sK2))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(sK2,sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,apply(sK2,sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102954,c_54505]) ).
tcf(c_105670,plain,
! [X0: $i] :
( in(apply(sK1,apply(sK2,sK21(sK1,sK2))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(sK2,sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(sK2,sK21(sK1,sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_105618,c_4013]) ).
tcf(c_105726,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_102956,c_49]) ).
tcf(c_105727,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2)))) = apply(relation_inverse(sK1),sK21(sK1,sK2)) )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102956,c_53]) ).
tcf(c_105728,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102956,c_52]) ).
tcf(c_105738,plain,
( in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102956,c_54665]) ).
tcf(c_105739,plain,
( in(ordered_pair(sK21(sK1,sK2),apply(relation_inverse(sK1),sK21(sK1,sK2))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102956,c_54505]) ).
tcf(c_105740,plain,
( ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102956,c_53757]) ).
tcf(c_105776,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),apply(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_105728,c_4013]) ).
tcf(c_105969,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK21(sK1,sK1)),sK21(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK21(sK1,sK1)) = sK22(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK21(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK21(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_29379,c_4838]) ).
tcf(c_106697,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK21(sK1,sK2)),sK21(sK1,sK2),sK1)
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_102957,c_49]) ).
tcf(c_106698,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2)))) = sK7(relation_inverse(sK1),sK21(sK1,sK2)) )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),sK7(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102957,c_53]) ).
tcf(c_106699,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))),relation_rng(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),sK7(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(superposition,[status(thm)],[c_102957,c_52]) ).
tcf(c_106709,plain,
( in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_rng(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(sK21(sK1,sK2),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102957,c_54665]) ).
tcf(c_106710,plain,
( in(ordered_pair(sK21(sK1,sK2),sK7(relation_inverse(sK1),sK21(sK1,sK2))),sK2)
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_102957,c_54505]) ).
tcf(c_106711,plain,
( ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK21(sK1,sK2)) = apply(sK2,sK21(sK1,sK2)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))) = empty_set ) ),
inference(superposition,[status(thm)],[c_102957,c_53757]) ).
tcf(c_106759,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,sK2))),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK7(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ~ sP0(sK1,sK21(sK1,sK2),sK7(relation_inverse(sK1),sK21(sK1,sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_106699,c_4013]) ).
tcf(c_106879,plain,
! [X0: $i] :
( sP0(X0,sK21(sK1,sK2),sK15(sK1,sK21(sK1,sK2)),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_102958,c_49]) ).
tcf(c_106880,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ in(sK21(sK1,sK2),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2),X0) ),
inference(superposition,[status(thm)],[c_102958,c_53]) ).
tcf(c_106881,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2),X0) ),
inference(superposition,[status(thm)],[c_102958,c_52]) ).
tcf(c_106932,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK21(sK1,sK2)),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ~ in(sK21(sK1,sK2),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_106881,c_3821,c_4030]) ).
tcf(c_106937,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK2 )
| ( apply(X0,apply(relation_inverse(sK1),sK21(sK1,sK2))) = sK21(sK1,sK2) )
| ~ in(sK21(sK1,sK2),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK21(sK1,sK2)),sK21(sK1,sK2),X0) ),
inference(light_normalisation,[status(thm)],[c_106880,c_4030]) ).
tcf(c_107280,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_7119,c_4997]) ).
tcf(c_107368,plain,
( in(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107280,c_64]) ).
tcf(c_107467,plain,
! [X0: $i] :
( sP0(X0,apply(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(apply(sK1,sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_29763,c_4838]) ).
tcf(c_108640,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK2),sK22(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_107368,c_70]) ).
tcf(c_108641,plain,
( element(sK22(sK1,sK1),relation_dom(sK2))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107368,c_69]) ).
tcf(c_108644,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( sK15(relation_inverse(sK1),sK15(sK1,sK22(sK1,sK1))) = apply(sK1,sK15(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_107368,c_12335]) ).
tcf(c_108645,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107368,c_8396]) ).
tcf(c_108646,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK15(sK1,sK22(sK1,sK1)))) = sK15(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_107368,c_8395]) ).
tcf(c_108647,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(sK2,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107368,c_4044]) ).
tcf(c_108648,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK2),sK22(sK1,sK1)) = apply(sK2,sK22(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(relation_inverse(sK2)) ),
inference(superposition,[status(thm)],[c_107368,c_42224]) ).
tcf(c_108649,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107368,c_12701]) ).
tcf(c_108650,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107368,c_10144]) ).
tcf(c_108651,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK15(sK1,sK22(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_107368,c_4468]) ).
tcf(c_108930,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK22(sK1,sK1)),empty_set,sK2)
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31401,c_49]) ).
tcf(c_108931,plain,
! [X0: $i] :
( ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(X0,apply(sK2,sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_31401,c_53]) ).
tcf(c_108932,plain,
! [X0: $i] :
( in(apply(sK2,sK7(sK1,sK22(sK1,sK1))),relation_rng(sK2))
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK1,sK22(sK1,sK1)) = sK7(sK1,sK22(sK1,sK1)) )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_dom(sK2))
| ~ sP0(sK2,empty_set,sK7(sK1,sK22(sK1,sK1)),X0) ),
inference(superposition,[status(thm)],[c_31401,c_52]) ).
tcf(c_110134,plain,
! [X0: $i] :
( sP0(X0,apply(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_108201,c_49]) ).
tcf(c_110135,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = sK1 )
| ( apply(X0,apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1)))) = apply(relation_inverse(sK1),sK22(sK2,sK1)) )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),apply(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(superposition,[status(thm)],[c_108201,c_53]) ).
tcf(c_110136,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))),relation_rng(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),apply(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(superposition,[status(thm)],[c_108201,c_52]) ).
tcf(c_110146,plain,
( in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108201,c_54665]) ).
tcf(c_110147,plain,
( in(ordered_pair(sK22(sK2,sK1),apply(relation_inverse(sK1),sK22(sK2,sK1))),sK2)
| ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108201,c_54505]) ).
tcf(c_110148,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(relation_inverse(sK1),sK22(sK2,sK1)) = apply(sK2,sK22(sK2,sK1)) )
| ( apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_108201,c_53757]) ).
tcf(c_110186,plain,
! [X0: $i] :
( in(apply(sK1,apply(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),apply(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_110136,c_4013]) ).
tcf(c_110298,plain,
! [X0: $i] :
( sP0(X0,sK7(relation_inverse(sK1),sK22(sK2,sK1)),sK22(sK2,sK1),sK1)
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_108202,c_49]) ).
tcf(c_110299,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = sK1 )
| ( apply(X0,apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1)))) = sK7(relation_inverse(sK1),sK22(sK2,sK1)) )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),sK7(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(superposition,[status(thm)],[c_108202,c_53]) ).
tcf(c_110300,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))),relation_rng(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),sK7(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(superposition,[status(thm)],[c_108202,c_52]) ).
tcf(c_110310,plain,
( in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_rng(sK2))
| ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(sK22(sK2,sK1),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108202,c_54665]) ).
tcf(c_110311,plain,
( in(ordered_pair(sK22(sK2,sK1),sK7(relation_inverse(sK1),sK22(sK2,sK1))),sK2)
| ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_108202,c_54505]) ).
tcf(c_110312,plain,
( ( relation_inverse(sK2) = sK1 )
| ( relation_inverse(sK1) = sK2 )
| ( sK7(relation_inverse(sK1),sK22(sK2,sK1)) = apply(sK2,sK22(sK2,sK1)) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))) = empty_set ) ),
inference(superposition,[status(thm)],[c_108202,c_53757]) ).
tcf(c_110362,plain,
! [X0: $i] :
( in(apply(sK1,sK7(relation_inverse(sK1),sK22(sK2,sK1))),relation_dom(sK2))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK7(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ~ sP0(sK1,sK22(sK2,sK1),sK7(relation_inverse(sK1),sK22(sK2,sK1)),X0) ),
inference(light_normalisation,[status(thm)],[c_110300,c_4013]) ).
tcf(c_110580,plain,
! [X0: $i] :
( sP0(X0,sK7(sK1,sK22(sK1,sK1)),sK22(sK1,sK1),relation_inverse(sK1))
| ( relation_inverse(sK1) = sK1 )
| ( apply(relation_inverse(sK1),sK22(sK1,sK1)) = sK21(sK1,sK1) )
| ( apply(sK2,sK7(sK1,sK22(sK1,sK1))) = empty_set )
| ~ in(sK7(sK1,sK22(sK1,sK1)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31403,c_4838]) ).
tcf(c_111224,plain,
! [X0: $i] :
( sP0(X0,sK22(sK2,sK1),sK15(sK1,sK22(sK2,sK1)),relation_inverse(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_108203,c_49]) ).
tcf(c_111225,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = sK1 )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) )
| ~ in(sK22(sK2,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1),X0) ),
inference(superposition,[status(thm)],[c_108203,c_53]) ).
tcf(c_111226,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_rng(relation_inverse(sK1)))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1),X0) ),
inference(superposition,[status(thm)],[c_108203,c_52]) ).
tcf(c_111277,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK22(sK2,sK1)),relation_dom(sK1))
| ( relation_inverse(sK2) = sK1 )
| ~ in(sK22(sK2,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_111226,c_3821,c_4030]) ).
tcf(c_111282,plain,
! [X0: $i] :
( ( relation_inverse(sK2) = sK1 )
| ( apply(X0,apply(relation_inverse(sK1),sK22(sK2,sK1))) = sK22(sK2,sK1) )
| ~ in(sK22(sK2,sK1),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),sK15(sK1,sK22(sK2,sK1)),sK22(sK2,sK1),X0) ),
inference(light_normalisation,[status(thm)],[c_111225,c_4030]) ).
tcf(c_111404,plain,
! [X0: $i] :
( sP0(X0,sK5(sK1,relation_rng(sK12)),empty_set,relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31465,c_49]) ).
tcf(c_111405,plain,
! [X0: $i] :
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK12),sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,sK5(sK1,relation_rng(sK12)),X0) ),
inference(superposition,[status(thm)],[c_31465,c_53]) ).
tcf(c_111406,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK12),sK5(sK1,relation_rng(sK12))),relation_rng(relation_inverse(sK12)))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,sK5(sK1,relation_rng(sK12)),X0) ),
inference(superposition,[status(thm)],[c_31465,c_52]) ).
tcf(c_111418,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK12),sK5(sK1,relation_rng(sK12))),relation_dom(sK12))
| ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,sK5(sK1,relation_rng(sK12)),X0) ),
inference(light_normalisation,[status(thm)],[c_111406,c_3810,c_3820]) ).
tcf(c_111424,plain,
! [X0: $i] :
( ( relation_rng(sK12) = relation_dom(sK1) )
| ( apply(sK1,sK5(sK1,relation_rng(sK12))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK12),sK5(sK1,relation_rng(sK12)))) = sK5(sK1,relation_rng(sK12)) )
| ~ in(sK5(sK1,relation_rng(sK12)),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,sK5(sK1,relation_rng(sK12)),X0) ),
inference(light_normalisation,[status(thm)],[c_111405,c_3810]) ).
tcf(c_112303,plain,
! [X0: $i] :
( in(sK22(X0,sK1),relation_dom(X0))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(X0) = sK1 )
| ( apply(sK2,apply(sK1,sK21(X0,sK1))) = sK21(X0,sK1) )
| ~ relation(X0) ),
inference(superposition,[status(thm)],[c_9069,c_4997]) ).
tcf(c_112317,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ relation(sK1) ),
inference(superposition,[status(thm)],[c_9069,c_4997]) ).
tcf(c_112401,plain,
( in(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_112317,c_64]) ).
tcf(c_112477,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112376,c_4997]) ).
tcf(c_112534,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112380,c_4997]) ).
tcf(c_112591,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK22(sK1,sK1)) = apply(sK1,sK22(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112384,c_4997]) ).
tcf(c_112836,plain,
! [X0: $i] :
( sP0(X0,sK13(sK1,relation_rng(sK12)),empty_set,relation_inverse(sK12))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31466,c_49]) ).
tcf(c_112837,plain,
! [X0: $i] :
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,sK13(sK1,relation_rng(sK12)),X0) ),
inference(superposition,[status(thm)],[c_31466,c_53]) ).
tcf(c_112838,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12))),relation_rng(relation_inverse(sK12)))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_dom(relation_inverse(sK12)))
| ~ sP0(relation_inverse(sK12),empty_set,sK13(sK1,relation_rng(sK12)),X0) ),
inference(superposition,[status(thm)],[c_31466,c_52]) ).
tcf(c_112850,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12))),relation_dom(sK12))
| ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,sK13(sK1,relation_rng(sK12)),X0) ),
inference(light_normalisation,[status(thm)],[c_112838,c_3810,c_3820]) ).
tcf(c_112856,plain,
! [X0: $i] :
( ( relation_rng(sK12) = relation_dom(sK2) )
| ( apply(sK2,sK13(sK1,relation_rng(sK12))) = empty_set )
| ( apply(X0,apply(relation_inverse(sK12),sK13(sK1,relation_rng(sK12)))) = sK13(sK1,relation_rng(sK12)) )
| ~ in(sK13(sK1,relation_rng(sK12)),relation_rng(sK12))
| ~ sP0(relation_inverse(sK12),empty_set,sK13(sK1,relation_rng(sK12)),X0) ),
inference(light_normalisation,[status(thm)],[c_112837,c_3810]) ).
tcf(c_113541,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ~ in(relation_dom(sK1),sK21(sK1,sK1)) ),
inference(superposition,[status(thm)],[c_112401,c_70]) ).
tcf(c_113542,plain,
( element(sK21(sK1,sK1),relation_dom(sK1))
| ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112401,c_69]) ).
tcf(c_113545,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112401,c_12766]) ).
tcf(c_113546,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112401,c_12765]) ).
tcf(c_113547,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1)))) = apply(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112401,c_10203]) ).
tcf(c_113548,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1)))) = sK7(sK1,sK21(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112401,c_10202]) ).
tcf(c_113549,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK15(sK1,apply(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112401,c_6249]) ).
tcf(c_113550,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK15(sK1,sK7(sK1,sK21(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112401,c_5349]) ).
tcf(c_113551,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112401,c_4997]) ).
tcf(c_113552,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( sK15(relation_inverse(sK1),sK21(sK1,sK1)) = apply(sK1,sK21(sK1,sK1)) )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112401,c_12284]) ).
tcf(c_113553,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112401,c_4619]) ).
tcf(c_113554,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK22(sK1,sK1))) = sK22(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) ) ),
inference(superposition,[status(thm)],[c_112401,c_4406]) ).
tcf(c_113619,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1))) = sK15(sK1,sK7(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112406,c_4997]) ).
tcf(c_113676,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1))) = sK15(sK1,apply(sK1,sK22(sK1,sK1))) ) ),
inference(superposition,[status(thm)],[c_112410,c_4997]) ).
tcf(c_113733,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112414,c_4997]) ).
tcf(c_113790,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,sK7(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112418,c_4997]) ).
tcf(c_113847,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),sK7(sK1,sK22(sK1,sK1)))) = sK7(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112422,c_4997]) ).
tcf(c_114015,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_inverse(sK1) = sK1 )
| ( apply(sK2,apply(sK1,sK21(sK1,sK1))) = sK21(sK1,sK1) )
| ( apply(sK1,apply(relation_inverse(sK1),apply(sK1,sK22(sK1,sK1)))) = apply(sK1,sK22(sK1,sK1)) ) ),
inference(superposition,[status(thm)],[c_112426,c_4997]) ).
tcf(c_115139,plain,
( ( relation_inverse(sK1) = sK2 )
| ( relation_rng(sK2) = relation_dom(sK2) )
| ( apply(sK1,sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(relation_inverse(sK1),sK13(sK1,relation_rng(sK2))) = empty_set )
| ( apply(sK2,apply(sK1,sK13(sK1,relation_rng(sK2)))) = empty_set ) ),
inference(superposition,[status(thm)],[c_54971,c_10569]) ).
tcf(c_115929,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_33899,c_12679]) ).
tcf(c_115935,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK6(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_32125,c_12679]) ).
tcf(c_115948,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))) = empty_set )
| ~ in(apply(sK1,sK15(sK1,sK20(relation_dom(sK2)))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_34151,c_12679]) ).
tcf(c_115949,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK24(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39302,c_12679]) ).
tcf(c_115950,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK24(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40624,c_12679]) ).
tcf(c_115960,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK21(sK1,empty_set))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_39676,c_12679]) ).
tcf(c_115961,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))) = empty_set )
| ~ in(apply(sK1,sK7(relation_inverse(sK1),sK22(empty_set,sK1))),relation_dom(sK2)) ),
inference(superposition,[status(thm)],[c_40100,c_12679]) ).
tcf(c_115986,plain,
( in(ordered_pair(sK15(sK1,sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115948,c_34151]) ).
tcf(c_115998,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( sK22(empty_set,sK1) = empty_set )
| ~ in(sK22(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115961,c_40100]) ).
tcf(c_115999,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK22(empty_set,sK1)),sK22(empty_set,sK1)),sK1)
| ( sK22(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_115998,c_40094]) ).
tcf(c_116002,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( sK21(sK1,empty_set) = empty_set )
| ~ in(sK21(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115960,c_39676]) ).
tcf(c_116003,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK21(sK1,empty_set)),sK21(sK1,empty_set)),sK1)
| ( sK21(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116002,c_39669]) ).
tcf(c_116006,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( sK24(empty_set,sK1) = empty_set )
| ~ in(sK24(empty_set,sK1),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115950,c_40624]) ).
tcf(c_116007,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(empty_set,sK1)),sK24(empty_set,sK1)),sK1)
| ( sK24(empty_set,sK1) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116006,c_40617]) ).
tcf(c_116010,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( sK24(sK1,empty_set) = empty_set )
| ~ in(sK24(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115949,c_39302]) ).
tcf(c_116011,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK24(sK1,empty_set)),sK24(sK1,empty_set)),sK1)
| ( sK24(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116010,c_39295]) ).
tcf(c_116014,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( sK6(sK1,empty_set) = empty_set )
| ~ in(sK6(sK1,empty_set),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115935,c_32125]) ).
tcf(c_116015,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK6(sK1,empty_set)),sK6(sK1,empty_set)),sK1)
| ( sK6(sK1,empty_set) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116014,c_32119]) ).
tcf(c_116018,plain,
( in(ordered_pair(sK7(relation_inverse(sK1),sK20(relation_dom(sK2))),sK20(relation_dom(sK2))),sK1)
| ( sK20(relation_dom(sK2)) = empty_set )
| ~ in(sK20(relation_dom(sK2)),relation_dom(sK2)) ),
inference(light_normalisation,[status(thm)],[c_115929,c_33899]) ).
tcf(c_117108,plain,
! [X0: $i] :
( sP0(X0,sK6(sK1,relation_dom(sK2)),empty_set,relation_inverse(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_31594,c_49]) ).
tcf(c_117109,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2)))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK6(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_31594,c_53]) ).
tcf(c_117110,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))),relation_rng(relation_inverse(sK1)))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(relation_inverse(sK1)))
| ~ sP0(relation_inverse(sK1),empty_set,sK6(sK1,relation_dom(sK2)),X0) ),
inference(superposition,[status(thm)],[c_31594,c_52]) ).
tcf(c_117179,plain,
! [X0: $i] :
( in(apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2))),relation_dom(sK1))
| ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK6(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_117110,c_3821,c_4030]) ).
tcf(c_117186,plain,
! [X0: $i] :
( ( relation_dom(sK1) = relation_dom(sK2) )
| ( sK15(sK1,sK6(sK1,relation_dom(sK2))) = sK5(sK1,relation_dom(sK2)) )
| ( apply(relation_inverse(sK1),sK5(sK1,relation_dom(sK2))) = sK15(sK1,sK5(sK1,relation_dom(sK2))) )
| ( apply(X0,apply(relation_inverse(sK1),sK6(sK1,relation_dom(sK2)))) = sK6(sK1,relation_dom(sK2)) )
| ~ in(sK6(sK1,relation_dom(sK2)),relation_dom(sK2))
| ~ sP0(relation_inverse(sK1),empty_set,sK6(sK1,relation_dom(sK2)),X0) ),
inference(light_normalisation,[status(thm)],[c_117109,c_4030]) ).
tcf(c_135128,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_126326,c_126325,c_126324,c_126323,c_126322,c_126321,c_126320,c_126319,c_126318,c_126317,c_126316,c_126315,c_126314,c_126313,c_126312,c_126311,c_126310,c_126309,c_117361,c_117360,c_117359,c_117358,c_117357,c_117356,c_117355,c_117354,c_117353,c_117352,c_117351,c_117350,c_117349,c_117348,c_117347,c_117346,c_117345,c_117344,c_117274,c_117273,c_117272,c_117271,c_117270,c_117269,c_117268,c_117267,c_117266,c_117265,c_117264,c_117263,c_117262,c_117261,c_117260,c_117259,c_117258,c_117257,c_117217,c_117216,c_117215,c_117214,c_117213,c_117212,c_117211,c_117210,c_117209,c_117208,c_117207,c_117206,c_117205,c_117204,c_117203,c_117202,c_117201,c_117200,c_117186,c_117179,c_117173,c_117172,c_117124,c_117123,c_117120,c_117112,c_117111,c_117110,c_117109,c_117108,c_117127,c_117126,c_117125,c_117121,c_117054,c_117053,c_117052,c_117051,c_117046,c_117045,c_117043,c_117042,c_117004,c_117002,c_117001,c_117000,c_116999,c_116998,c_116997,c_116996,c_116995,c_116994,c_116993,c_116990,c_116989,c_116947,c_116946,c_116945,c_116944,c_116943,c_116942,c_116941,c_116940,c_116939,c_116938,c_116937,c_116936,c_116935,c_116934,c_116933,c_116932,c_116931,c_116930,c_116577,c_116576,c_116575,c_116574,c_116573,c_116572,c_116571,c_116570,c_116569,c_116568,c_116567,c_116566,c_116565,c_116564,c_116563,c_116562,c_116561,c_116560,c_116479,c_116478,c_116477,c_116476,c_116475,c_116474,c_116473,c_116472,c_116471,c_116470,c_116469,c_116468,c_116467,c_116466,c_116465,c_116464,c_116463,c_116462,c_116386,c_116385,c_116384,c_116383,c_116382,c_116381,c_116380,c_116379,c_116378,c_116377,c_116376,c_116375,c_116374,c_116373,c_116372,c_116371,c_116370,c_116369,c_116018,c_116015,c_116014,c_116011,c_116010,c_116007,c_116006,c_116003,c_116002,c_115999,c_115998,c_115986,c_115968,c_115967,c_115966,c_115962,c_115961,c_115960,c_115959,c_115957,c_115956,c_115955,c_115954,c_115950,c_115949,c_115948,c_115947,c_115946,c_115945,c_115944,c_115943,c_115942,c_115941,c_115940,c_115939,c_115936,c_115935,c_115934,c_115933,c_115932,c_115931,c_115930,c_115929,c_115924,c_115923,c_115897,c_115896,c_115888,c_115844,c_115842,c_115841,c_115840,c_115839,c_115838,c_115837,c_115836,c_115835,c_115834,c_115833,c_115830,c_115829,c_115797,c_115795,c_115794,c_115793,c_115792,c_115791,c_115790,c_115789,c_115788,c_115787,c_115786,c_115783,c_115782,c_115750,c_115748,c_115747,c_115746,c_115745,c_115744,c_115743,c_115742,c_115741,c_115740,c_115739,c_115736,c_115735,c_115703,c_115701,c_115700,c_115699,c_115698,c_115697,c_115696,c_115695,c_115694,c_115693,c_115692,c_115689,c_115688,c_115448,c_115447,c_115446,c_115445,c_115444,c_115443,c_115442,c_115441,c_115440,c_115439,c_115438,c_115437,c_115436,c_115435,c_115434,c_115433,c_115432,c_115431,c_115391,c_115390,c_115389,c_115388,c_115387,c_115386,c_115385,c_115384,c_115383,c_115382,c_115381,c_115380,c_115379,c_115378,c_115377,c_115376,c_115375,c_115374,c_115334,c_115333,c_115332,c_115331,c_115330,c_115329,c_115328,c_115327,c_115326,c_115325,c_115324,c_115323,c_115322,c_115321,c_115320,c_115319,c_115318,c_115317,c_115227,c_115226,c_115225,c_115224,c_115223,c_115222,c_115221,c_115220,c_115219,c_115218,c_115217,c_115216,c_115215,c_115214,c_115213,c_115212,c_115211,c_115210,c_115142,c_115141,c_115139,c_115138,c_115135,c_115134,c_115133,c_115132,c_115029,c_115013,c_115010,c_115006,c_114990,c_114989,c_114988,c_114987,c_114986,c_114985,c_114984,c_114948,c_114946,c_114945,c_114944,c_114943,c_114942,c_114941,c_114940,c_114939,c_114938,c_114937,c_114934,c_114933,c_114874,c_114872,c_114871,c_114870,c_114869,c_114868,c_114867,c_114866,c_114865,c_114864,c_114863,c_114860,c_114859,c_114827,c_114825,c_114824,c_114823,c_114822,c_114821,c_114820,c_114819,c_114818,c_114817,c_114816,c_114813,c_114812,c_114553,c_114551,c_114550,c_114549,c_114548,c_114547,c_114546,c_114545,c_114544,c_114543,c_114542,c_114539,c_114538,c_114496,c_114495,c_114494,c_114493,c_114492,c_114491,c_114490,c_114489,c_114488,c_114487,c_114486,c_114485,c_114484,c_114483,c_114482,c_114481,c_114480,c_114479,c_114439,c_114438,c_114437,c_114436,c_114435,c_114434,c_114433,c_114432,c_114431,c_114430,c_114429,c_114428,c_114427,c_114426,c_114425,c_114424,c_114423,c_114422,c_114382,c_114381,c_114380,c_114379,c_114378,c_114377,c_114376,c_114375,c_114374,c_114373,c_114372,c_114371,c_114370,c_114369,c_114368,c_114367,c_114366,c_114365,c_114325,c_114324,c_114323,c_114322,c_114321,c_114320,c_114319,c_114318,c_114317,c_114316,c_114315,c_114314,c_114313,c_114312,c_114311,c_114310,c_114309,c_114308,c_114111,c_114083,c_114079,c_114077,c_114076,c_114075,c_114074,c_114073,c_114072,c_114070,c_114069,c_114068,c_114067,c_114018,c_114017,c_114016,c_114015,c_114014,c_114013,c_114012,c_114011,c_114010,c_114009,c_114006,c_114005,c_113850,c_113849,c_113848,c_113847,c_113846,c_113845,c_113844,c_113843,c_113842,c_113841,c_113838,c_113837,c_113793,c_113792,c_113791,c_113790,c_113789,c_113788,c_113787,c_113786,c_113785,c_113784,c_113781,c_113780,c_113736,c_113735,c_113734,c_113733,c_113732,c_113731,c_113730,c_113729,c_113728,c_113727,c_113724,c_113723,c_113679,c_113678,c_113677,c_113676,c_113675,c_113674,c_113673,c_113672,c_113671,c_113670,c_113667,c_113666,c_113622,c_113621,c_113620,c_113619,c_113618,c_113617,c_113616,c_113615,c_113614,c_113613,c_113610,c_113609,c_113554,c_113553,c_113552,c_113551,c_113550,c_113549,c_113548,c_113547,c_113546,c_113545,c_113542,c_113541,c_113344,c_113342,c_113341,c_113340,c_113339,c_113338,c_113337,c_113336,c_113335,c_113334,c_113333,c_113330,c_113329,c_113297,c_113295,c_113294,c_113293,c_113292,c_113291,c_113290,c_113289,c_113288,c_113287,c_113286,c_113283,c_113282,c_113188,c_113186,c_113185,c_113184,c_113183,c_113182,c_113181,c_113180,c_113179,c_113178,c_113177,c_113174,c_113173,c_113110,c_113109,c_113108,c_113107,c_113106,c_113105,c_113104,c_113103,c_113102,c_113101,c_113100,c_113099,c_113098,c_113097,c_113096,c_113095,c_113094,c_113093,c_113053,c_113052,c_113051,c_113050,c_113049,c_113048,c_113047,c_113046,c_113045,c_113044,c_113043,c_113042,c_113041,c_113040,c_113039,c_113038,c_113037,c_113036,c_112968,c_112967,c_112966,c_112965,c_112964,c_112963,c_112962,c_112961,c_112960,c_112959,c_112958,c_112957,c_112956,c_112955,c_112954,c_112953,c_112952,c_112951,c_112886,c_112885,c_112884,c_112883,c_112882,c_112881,c_112880,c_112879,c_112878,c_112877,c_112876,c_112875,c_112874,c_112873,c_112872,c_112871,c_112870,c_112869,c_112856,c_112850,c_112845,c_112844,c_112839,c_112838,c_112837,c_112836,c_112594,c_112593,c_112592,c_112591,c_112590,c_112589,c_112588,c_112587,c_112586,c_112585,c_112582,c_112581,c_112537,c_112536,c_112535,c_112534,c_112533,c_112532,c_112531,c_112530,c_112529,c_112528,c_112525,c_112524,c_112480,c_112479,c_112478,c_112477,c_112476,c_112475,c_112474,c_112473,c_112472,c_112471,c_112468,c_112467,c_112426,c_112422,c_112418,c_112414,c_112410,c_112406,c_112401,c_112384,c_112380,c_112376,c_112371,c_112366,c_112361,c_112357,c_112356,c_112332,c_112329,c_112325,c_112320,c_112319,c_112318,c_112317,c_112316,c_112315,c_112314,c_112313,c_112312,c_112311,c_112309,c_112308,c_112307,c_112306,c_112305,c_112304,c_112303,c_112302,c_112301,c_112300,c_112299,c_112298,c_112297,c_112294,c_112293,c_112292,c_112291,c_112290,c_112289,c_112271,c_112270,c_112265,c_112260,c_112255,c_112239,c_112235,c_112233,c_112232,c_112231,c_112230,c_112229,c_112228,c_112226,c_112225,c_112224,c_112223,c_112182,c_112180,c_112179,c_112178,c_112177,c_112176,c_112175,c_112174,c_112173,c_112172,c_112171,c_112168,c_112167,c_111987,c_111985,c_111984,c_111983,c_111982,c_111981,c_111980,c_111979,c_111978,c_111977,c_111976,c_111973,c_111972,c_111940,c_111938,c_111937,c_111936,c_111935,c_111934,c_111933,c_111932,c_111931,c_111930,c_111929,c_111926,c_111925,c_111838,c_111837,c_111836,c_111835,c_111834,c_111833,c_111832,c_111831,c_111830,c_111829,c_111828,c_111827,c_111826,c_111825,c_111824,c_111823,c_111822,c_111821,c_111781,c_111780,c_111779,c_111778,c_111777,c_111776,c_111775,c_111774,c_111773,c_111772,c_111771,c_111770,c_111769,c_111768,c_111767,c_111766,c_111765,c_111764,c_111525,c_111524,c_111523,c_111522,c_111521,c_111520,c_111519,c_111518,c_111517,c_111516,c_111515,c_111514,c_111513,c_111512,c_111511,c_111510,c_111509,c_111508,c_111454,c_111453,c_111452,c_111451,c_111450,c_111449,c_111448,c_111447,c_111446,c_111445,c_111444,c_111443,c_111442,c_111441,c_111440,c_111439,c_111438,c_111437,c_111424,c_111418,c_111413,c_111412,c_111407,c_111406,c_111405,c_111404,c_111382,c_111381,c_111380,c_111378,c_111375,c_111374,c_111364,c_111358,c_111282,c_111277,c_111273,c_111272,c_111241,c_111240,c_111239,c_111235,c_111234,c_111233,c_111232,c_111229,c_111228,c_111227,c_111226,c_111225,c_111224,c_111205,c_111204,c_111199,c_111197,c_111196,c_111195,c_111163,c_111161,c_111160,c_111159,c_111158,c_111157,c_111156,c_111155,c_111154,c_111153,c_111152,c_111149,c_111148,c_111116,c_111114,c_111113,c_111112,c_111111,c_111110,c_111109,c_111108,c_111107,c_111106,c_111105,c_111102,c_111101,c_110937,c_110935,c_110934,c_110933,c_110932,c_110931,c_110930,c_110929,c_110928,c_110927,c_110926,c_110923,c_110922,c_110890,c_110888,c_110887,c_110886,c_110885,c_110884,c_110883,c_110882,c_110881,c_110880,c_110879,c_110876,c_110875,c_110833,c_110832,c_110831,c_110830,c_110829,c_110828,c_110827,c_110826,c_110825,c_110824,c_110823,c_110822,c_110821,c_110820,c_110819,c_110818,c_110817,c_110816,c_110776,c_110775,c_110774,c_110773,c_110772,c_110771,c_110770,c_110769,c_110768,c_110767,c_110766,c_110765,c_110764,c_110763,c_110762,c_110761,c_110760,c_110759,c_110719,c_110718,c_110717,c_110716,c_110715,c_110714,c_110713,c_110712,c_110711,c_110710,c_110709,c_110708,c_110707,c_110706,c_110705,c_110704,c_110703,c_110702,c_110662,c_110661,c_110660,c_110659,c_110658,c_110657,c_110656,c_110655,c_110654,c_110653,c_110652,c_110651,c_110650,c_110649,c_110648,c_110647,c_110646,c_110645,c_110632,c_110592,c_110589,c_110587,c_110586,c_110584,c_110583,c_110581,c_110580,c_110579,c_110578,c_110362,c_110341,c_110316,c_110312,c_110311,c_110310,c_110308,c_110307,c_110306,c_11030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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU218+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.58 % Computer : n004.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Thu Sep 24 13:14:28 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.11/5.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.62 Running first-order theorem proving
% 0.15/5.62 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
% 0.15/5.63
% 0.15/5.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.63
% 0.15/5.63 % Detected problem language: tptp
% 0.15/5.64 % Proving...
% 90.88/18.68 % SZS status Started for theBenchmark.p
% 90.88/18.68 % SZS status Theorem for theBenchmark.p
% 90.88/18.68
% 90.88/18.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 90.88/18.68
% 90.88/18.68 % ------ iProver source info
% 90.88/18.68
% 90.88/18.68 % git: date: 2026-07-19 20:42:38 +0200
% 90.88/18.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 90.88/18.68 % git: non_committed_changes: false
% 90.88/18.68
% 90.88/18.68 % ------ Parsing...
% 90.88/18.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 90.88/18.68
% 90.88/18.68 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 7 sf_s rm: 2 0s sf_e pe_s pe_e %
% 90.88/18.68
% 90.88/18.68 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 90.88/18.68
% 90.88/18.68 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 90.88/18.68 % ------ Proving...
% 90.88/18.68 % ------ Problem Properties
% 90.88/18.68
% 90.88/18.68 %
% 90.88/18.68 % clauses 85
% 90.88/18.68 % conjectures 4
% 90.88/18.68 % EPR 27
% 90.88/18.68 % Horn 72
% 90.88/18.68 % unary 28
% 90.88/18.68 % binary 25
% 90.88/18.68 % lits 193
% 90.88/18.68 % lits eq 34
% 90.88/18.68 % fd_pure 0
% 90.88/18.68 % fd_pseudo 0
% 90.88/18.68 % fd_cond 1
% 90.88/18.68 % fd_pseudo_cond 11
% 90.88/18.68 % AC symbols 0
% 90.88/18.68
% 90.88/18.68 % ------ Schedule dynamic 5 is on
% 90.88/18.68
% 90.88/18.68 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 90.88/18.68
% 90.88/18.68
% 90.88/18.68 % ------
% 90.88/18.68 % Current options:
% 90.88/18.68 % ------
% 90.88/18.68
% 90.88/18.68
% 90.88/18.68 %
% 90.88/18.68
% 90.88/18.68 % ------ Proving...
% 90.88/18.68 %
% 90.88/18.68
% 90.88/18.68 % SZS status Theorem for theBenchmark.p
% 90.88/18.68
% 90.88/18.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 91.62/18.88
% 91.62/18.88
%------------------------------------------------------------------------------